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This page provides a list of all articles available at PlanetMath in the following topic:

54-XX General topology.

This list will be periodically updated. Each entry in the list has three fields:

  1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
  2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
  3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status means PM article
N not needed
A adequately covered
C copied
M merged
NC needs copying
NM needs merging
  • Please update the WP and Status fields as appropriate.
  • if the WP field is correct please remove the qualifier "guess".
  • If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
  • If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
  • If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.

Don't forget to include the relevant template if you copy over text or feel like an external link is warranted

  • {{planetmath|id=|title=}} for copied over text
  • {{planetmath reference|id=|title=}} for an external link

See the main page for examples and usage criteria.

One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.

54-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

[edit]
Do we want to start creating Bibliograhies? Paul August ☎ 20:15, Feb 1, 2005 (UTC)
Paul August ☎ 20:15, Feb 1, 2005 (UTC)
The PM article does have a proof of some equivalent conditions to connected, but I don't really think we need it. Paul August ☎ 04:35, Feb 2, 2005 (UTC)
Paul August ☎ 04:08, Mar 14, 2005 (UTC)
Paul August ☎ 04:53, Feb 2, 2005 (UTC)
still A linas (talk) 04:20, 11 June 2009 (UTC)[reply]
Completely normal redirects to normal space, but I think it could have its own article. Paul August ☎ 03:21, 1 September 2006 (UTC)[reply]
AdamSmithee 14:31, 16 January 2006 (UTC)[reply]
AdamSmithee 14:31, 16 January 2006 (UTC)[reply]
Paul August ☎ 20:21, 3 September 2006 (UTC)[reply]
Paul August ☎ 03:27, 1 September 2006 (UTC)[reply]
Paul August ☎ 17:28, 17 October 2006 (UTC)[reply]
Paul August ☎ 18:38, 23 October 2006 (UTC)[reply]
Paul August ☎ 04:11, 1 September 2006 (UTC)[reply]
The interior operator stuff uses a nicer notation in PM AdamSmithee 14:31, 16 January 2006 (UTC)[reply]
Change to NM, the nicer PM layout should be merged in. linas 16:36, 26 November 2006 (UTC)[reply]
Paul August ☎ 04:11, 7 August 2007 (UTC)[reply]
I can't find this anywhere else, so probably not particularly notable. Paul August ☎ 16:26, 7 August 2007 (UTC)[reply]
Paul August ☎ 19:22, 1 September 2006 (UTC)[reply]
Loop (topology) redirects to Path (topology), but it could have it's own article. Paul August ☎ 19:52, 1 September 2006 (UTC)[reply]
linas 13:43, 4 March 2007 (UTC)[reply]
Paul August ☎ 01:45, 23 October 2006 (UTC)[reply]
AdamSmithee 14:31, 16 January 2006 (UTC)[reply]
Paul August ☎ 04:22, 3 September 2006 (UTC)[reply]
WP article has materialized. linas 14:42, 4 March 2007 (UTC)[reply]
Paul August ☎ 20:13, 1 September 2006 (UTC)[reply]
Paul August ☎ 02:38, 23 October 2006 (UTC)[reply]
Paul August ☎ 03:57, 3 September 2006 (UTC)[reply]
Oleg Alexandrov (talk) 02:05, 24 July 2006 (UTC)[reply]
Paul August ☎ 03:54, 3 September 2006 (UTC)[reply]
Regular open set redirects to topological glossary, but could have its own article.
Properties, particularly 5 and 6 AdamSmithee 14:31, 16 January 2006 (UTC)[reply]
AdamSmithee 14:31, 16 January 2006 (UTC)[reply]
AdamSmithee 14:31, 16 January 2006 (UTC)[reply]
May deserve its own article. Paul August ☎ 17:11, 7 August 2007 (UTC)[reply]
Paul August ☎ 20:30, 3 September 2006 (UTC)[reply]
Paul August ☎ 02:52, 23 October 2006 (UTC)[reply]
Paul August ☎ 20:03, 23 October 2006 (UTC)[reply]
Paul August ☎ 20:17, 23 October 2006 (UTC)[reply]
Paul August ☎ 03:38, 6 September 2006 (UTC)[reply]

54A05 Topological spaces and generalizations (closure spaces, etc.)

[edit]
Paul August ☎ 03:04, 9 September 2006 (UTC)[reply]
Paul August ☎ 03:04, 9 September 2006 (UTC)[reply]
Paul August ☎ 05:00, 11 August 2007 (UTC)[reply]
Paul August ☎ 23:19, 28 October 2006 (UTC)[reply]
AdamSmithee 14:51, 16 January 2006 (UTC)[reply]
Paul August ☎ 05:00, 24 October 2006 (UTC)[reply]
AdamSmithee 14:51, 16 January 2006 (UTC)[reply]
Paul August ☎ 03:22, 11 August 2007 (UTC)[reply]
Paul August ☎ 01:44, 13 August 2007 (UTC)[reply]
Paul August ☎ 02:00, 13 August 2007 (UTC)[reply]
Paul August ☎ 02:14, 20 August 2007 (UTC)[reply]

54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)

[edit]

54A15 Syntopogeneous structures

[edit]

54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)

[edit]
Paul August ☎ 02:36, 14 August 2007 (UTC)[reply]
Paul August ☎ 05:06, 24 October 2006 (UTC)[reply]
Paul August ☎ 02:33, 14 August 2007 (UTC)[reply]
linas 00:06, 22 November 2006 (UTC)[reply]
Paul August ☎ 02:37, 14 August 2007 (UTC)[reply]
Paul August ☎ 01:40, 13 August 2007 (UTC)[reply]
linas 00:09, 22 November 2006 (UTC)[reply]

54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)

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54A99 Miscellaneous

[edit]
linas 04:08, 27 November 2006 (UTC)[reply]
linas 21:49, 24 November 2006 (UTC)[reply]
linas 00:36, 22 November 2006 (UTC)[reply]
AdamSmithee 15:11, 16 January 2006 (UTC)[reply]
Paul August ☎ 01:32, 8 August 2007 (UTC)[reply]
AdamSmithee 15:11, 16 January 2006 (UTC)[reply]
Physicistjedi 05:06, December 8 2006 (UTC)
Paul August ☎ 01:42, 8 August 2007 (UTC)[reply]
I especially like the wording where PM explains the meaning of limit in the name limit point AdamSmithee 15:11, 16 January 2006 (UTC)[reply]
linas 23:48, 24 November 2006 (UTC)[reply]
AdamSmithee 15:11, 16 January 2006 (UTC)[reply]
linas 21:54, 24 November 2006 (UTC)[reply]
AdamSmithee 15:11, 16 January 2006 (UTC)[reply]
Paul August ☎ 02:21, 20 August 2007 (UTC)[reply]

54Axx Generalities

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54B05 Subspaces

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Paul August ☎ 02:47, 14 August 2007 (UTC)[reply]
Paul August ☎ 02:48, 14 August 2007 (UTC)[reply]
Paul August ☎ 02:51, 14 August 2007 (UTC)[reply]
Paul August ☎ 02:54, 14 August 2007 (UTC)[reply]
Paul August ☎ 02:56, 14 August 2007 (UTC)[reply]

54B10 Product spaces

[edit]
linas 00:28, 22 November 2006 (UTC)[reply]
Article is a proof, added a link to it in product topology. linas 00:40, 22 November 2006 (UTC)[reply]
Article is a proof, added a link to it in initial topology. linas 01:14, 26 November 2006 (UTC)[reply]

54B15 Quotient spaces, decompositions

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Paul August ☎ 03:05, 27 July 2007 (UTC)[reply]
linas 20:38, 25 November 2006 (UTC)[reply]

54B17 Adjunction spaces and similar constructions

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linas 01:34, 26 November 2006 (UTC)[reply]

54B40 Presheaves and sheaves

[edit]
Copied by Jtwdog. Paul August ☎ 00:10, 28 July 2007 (UTC)[reply]

54B99 Miscellaneous

[edit]
linas 19:03, 24 November 2006 (UTC)[reply]
WP article is missing definition of a reduced cone on pointed spaces.linas 21:49, 25 November 2006 (UTC)[reply]
Now Merged. linas 02:10, 26 November 2006 (UTC)[reply]
linas 22:00, 25 November 2006 (UTC)[reply]
Previously merged by User:Lethe in Dec 2005.
linas 02:02, 26 November 2006 (UTC)[reply]
linas 17:02, 25 November 2006 (UTC)[reply]

54Bxx Basic constructions

[edit]

54C05 Continuous maps

[edit]
Paul August ☎ 00:20, 28 July 2007 (UTC)[reply]

54C08 Weak and generalized continuity

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54C10 Special maps on topological spaces (open, closed, perfect, etc.)

[edit]
Paul August ☎ 02:54, 28 July 2007 (UTC)[reply]

54C15 Retraction

[edit]
linas 23:36, 24 November 2006 (UTC)[reply]

54C20 Extension of maps

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Added as link in article. linas 23:39, 24 November 2006 (UTC)[reply]

54C25 Embedding

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54C30 Real-valued functions

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54C35 Function spaces

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54C40 Algebraic properties of function spaces

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54C45 $C$- and $C^*$-embedding

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54C50 Special sets defined by functions

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54C70 Entropy

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54C99 Miscellaneous

[edit]
Paul August ☎ 02:57, 30 July 2007 (UTC)[reply]

54Cxx Maps and general types of spaces defined by maps

[edit]

54D05 Connected and locally connected spaces (general aspects)

[edit]
Paul August ☎ 03:00, 30 July 2007 (UTC)[reply]
Paul August ☎ 03:02, 30 July 2007 (UTC)[reply]
Paul August ☎ 04:48, 30 July 2007 (UTC)[reply]
Paul August ☎ 04:49, 30 July 2007 (UTC)[reply]
Paul August ☎ 04:52, 30 July 2007 (UTC)[reply]
Paul August ☎ 00:14, 1 August 2007 (UTC)[reply]
Paul August ☎ 00:44, 1 August 2007 (UTC)[reply]
Paul August ☎ 00:51, 1 August 2007 (UTC)[reply]
Paul August ☎ 01:01, 1 August 2007 (UTC)[reply]
linas 17:17, 24 November 2006 (UTC)[reply]
Paul August ☎ 00:34, 1 August 2007 (UTC)[reply]
Paul August ☎ 00:39, 1 August 2007 (UTC)[reply]
  • PM: path, id=942 -- WP guess: path -- Status:
linas 17:27, 24 November 2006 (UTC)[reply]

54D10 Lower separation axioms (T0--T3, etc.)

[edit]
Paul August ☎ 03:41, 1 August 2007 (UTC)[reply]
Paul August ☎ 03:44, 1 August 2007 (UTC)[reply]
Paul August ☎ 03:46, 1 August 2007 (UTC)[reply]
Paul August ☎ 03:54, 1 August 2007 (UTC)[reply]
21:08, 1 August 2007 (UTC)
linas 19:35, 24 November 2006 (UTC)[reply]
Nice counterexample. linas 19:44, 24 November 2006 (UTC)[reply]
This is a proof of a theorem, and was linked as such in metric space. linas 18:44, 22 November 2006 (UTC)[reply]
A proof, added as link to Hausdorff space. linas 02:32, 26 November 2006 (UTC)[reply]
This is a proof, added link to article on Hausdorff space. linas 02:26, 26 November 2006 (UTC)[reply]
linas 20:18, 24 November 2006 (UTC)[reply]
linas 02:35, 26 November 2006 (UTC)[reply]
linas 19:53, 24 November 2006 (UTC)[reply]
linas 20:01, 24 November 2006 (UTC)[reply]
linas 20:05, 24 November 2006 (UTC)[reply]
linas 20:07, 24 November 2006 (UTC)[reply]
Paul August ☎ 21:15, 1 August 2007 (UTC)[reply]
Its a proof, added as a link to Hausdorff space. linas 02:39, 26 November 2006 (UTC)[reply]

54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

[edit]
linas 20:26, 24 November 2006 (UTC)[reply]
linas 20:27, 24 November 2006 (UTC)[reply]
Added as link from Urysohn's lemma. linas 20:52, 24 November 2006 (UTC)[reply]
linas 20:58, 24 November 2006 (UTC)[reply]
linas 21:19, 24 November 2006 (UTC)[reply]
linas 20:41, 24 November 2006 (UTC)[reply]

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)

[edit]
linas 15:26, 4 March 2007 (UTC)[reply]
linas 17:25, 19 November 2006 (UTC)[reply]
linas 15:19, 4 March 2007 (UTC)[reply]
PM is dictdef, WP is link to glossary. linas 22:35, 24 November 2006 (UTC)[reply]
PM object 6256 is "not found"; however, I did copy obj id 8398, point finite from PM. linas 14:52, 4 March 2007 (UTC)[reply]

54D30 Compactness

[edit]
Proof of something that seems shallow. linas 15:37, 4 March 2007 (UTC)[reply]
Proof, added as a reference to compact space and finite intersection property linas 15:46, 4 March 2007 (UTC)[reply]
Proof, added as a reference to compact space. linas 16:06, 4 March 2007 (UTC)[reply]
Proof, added as a reference to compact space. linas 16:16, 4 March 2007 (UTC)[reply]
linas 15:28, 4 March 2007 (UTC)[reply]
Proof, added as a reference to compact space. linas 16:25, 4 March 2007 (UTC)[reply]
Merged. linas 16:34, 4 March 2007 (UTC)[reply]
linas 16:03, 4 March 2007 (UTC)[reply]
AdamSmithee 15:18, 16 January 2006 (UTC)[reply]
linas 20:08, 4 March 2007 (UTC)[reply]
AdamSmithee 15:18, 16 January 2006 (UTC)[reply]
Proof, added as a reference to Heine-Borel theorem linas 20:15, 4 March 2007 (UTC)[reply]
linas 20:17, 4 March 2007 (UTC)[reply]
linas 20:26, 4 March 2007 (UTC)[reply]
Actually, obj id 4722 is "not found" on PM linas 20:35, 4 March 2007 (UTC)[reply]
linas 21:00, 4 March 2007 (UTC)[reply]
linas 21:39, 4 March 2007 (UTC)[reply]
linas 21:22, 24 November 2006 (UTC)[reply]
linas 20:46, 4 March 2007 (UTC)[reply]
Linked proof to Tychonoff's theorem linas 21:29, 24 November 2006 (UTC)[reply]

54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)

[edit]
This content is contained in [[compactification (mathematics), but probably should have its own article. Paul August ☎ 04:56, 2 August 2007 (UTC)[reply]
Paul August ☎ 05:19, 2 August 2007 (UTC)[reply]

54D45 Local compactness, $\sigma$-compactness

[edit]
Paul August ☎ 05:26, 2 August 2007 (UTC)[reply]
Paul August ☎ 05:33, 2 August 2007 (UTC)[reply]
Note what PM calls "precompact", WP calls "relatively compact". Paul August ☎ 05:56, 2 August 2007 (UTC)[reply]

54D65 Separability

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linas 18:35, 22 November 2006 (UTC)[reply]

54D70 Base properties

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linas 22:07, 24 November 2006 (UTC)[reply]
linas 22:09, 24 November 2006 (UTC)[reply]

54D99 Miscellaneous

[edit]
linas 18:33, 22 November 2006 (UTC)[reply]
Paul August ☎ 22:36, 2 August 2007 (UTC)[reply]
Paul August ☎ 22:36, 2 August 2007 (UTC)[reply]
Paul August ☎ 16:11, 7 August 2007 (UTC)[reply]

54Dxx Fairly general properties

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54E05 Proximity structures and generalizations

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linas 16:12, 19 November 2006 (UTC)[reply]

54E15 Uniform structures and generalizations

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Paul August ☎ 03:29, 4 August 2007 (UTC)[reply]
Paul August ☎ 03:24, 4 August 2007 (UTC)[reply]
Paul August ☎ 03:36, 4 August 2007 (UTC)[reply]
Paul August ☎ 03:36, 4 August 2007 (UTC)[reply]

54E17 Nearness spaces

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54E25 Semimetric spaces

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linas 06:37, 22 November 2006 (UTC)[reply]
PM article is blanked, because it gave the wrong definition (it confused quasimetric with semi-metric). linas 06:19, 22 November 2006 (UTC)[reply]
The PM article has now been fixed. Paul August ☎ 03:40, 4 August 2007 (UTC)[reply]

54E30 Moore spaces

[edit]
Paul August ☎ 04:01, 4 August 2007 (UTC)[reply]

54E35 Metric spaces, metrizability

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Paul August ☎ 04:24, 4 August 2007 (UTC)[reply]
Paul August ☎ 04:31, 4 August 2007 (UTC)[reply]
Paul August ☎ 04:38, 4 August 2007 (UTC)[reply]
Paul August ☎ 04:37, 4 August 2007 (UTC)[reply]
Paul August ☎ 04:39, 4 August 2007 (UTC)[reply]
Paul August ☎ 05:00, 4 August 2007 (UTC)[reply]
Paul August ☎ 05:04, 4 August 2007 (UTC)[reply]
linas 18:24, 22 November 2006 (UTC)[reply]
Paul August ☎ 05:17, 4 August 2007 (UTC)[reply]
linas 17:07, 24 November 2006 (UTC)[reply]
Paul August ☎ 02:33, 17 August 2007 (UTC)[reply]
Paul August ☎ 05:28, 4 August 2007 (UTC)[reply]
linas 18:27, 22 November 2006 (UTC)[reply]
Paul August ☎ 05:31, 4 August 2007 (UTC)[reply]
Paul August ☎ 01:35, 6 August 2007 (UTC)[reply]
linas 16:20, 22 November 2006 (UTC)[reply]
Mostly a proof, which is now referenced in the topology subsection of pseudometric space. linas 16:33, 22 November 2006 (UTC)[reply]
linas 06:46, 22 November 2006 (UTC)[reply]
Paul August ☎ 04:31, 5 August 2007 (UTC)[reply]
Paul August ☎ 04:58, 5 August 2007 (UTC)[reply]
Paul August ☎ 05:20, 5 August 2007 (UTC)[reply]
Paul August ☎ 01:28, 6 August 2007 (UTC)[reply]
Paul August ☎ 01:38, 6 August 2007 (UTC)[reply]
linas 19:29, 22 November 2006 (UTC)[reply]

54E40 Special maps on metric spaces

[edit]
linas 22:12, 24 November 2006 (UTC)[reply]

54E45 Compact (locally compact) metric spaces

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Paul August ☎ 01:43, 6 August 2007 (UTC)[reply]
Paul August ☎ 01:43, 6 August 2007 (UTC)[reply]
Paul August ☎ 01:55, 6 August 2007 (UTC)[reply]

54E50 Complete metric spaces

[edit]
Paul August ☎ 01:58, 6 August 2007 (UTC)[reply]
Paul August ☎ 02:08, 6 August 2007 (UTC)[reply]
Paul August ☎ 02:15, 6 August 2007 (UTC)[reply]
Paul August ☎ 03:32, 27 August 2006 (UTC)[reply]
Paul August ☎ 03:28, 27 August 2006 (UTC)[reply]

54E52 Baire category, Baire spaces

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linas 18:13, 19 November 2006 (UTC)[reply]
Paul August ☎ 02:22, 6 August 2007 (UTC)[reply]
Paul August ☎ 02:51, 6 August 2007 (UTC)[reply]

54E70 Probabilistic metric spaces

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54E99 Miscellaneous

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Kompik 11:32, 22 February 2006 (UTC)[reply]
Paul August ☎ 03:13, 27 August 2006 (UTC)[reply]
Paul August ☎ 01:16, 25 July 2007 (UTC)[reply]

54Exx Spaces with richer structures

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54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

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54F45 Dimension theory

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54F65 Topological characterizations of particular spaces

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54F99 Miscellaneous

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54Fxx Special properties

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54G05 Extremally disconnected spaces, $F$-spaces, etc.

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Paul August ☎ 03:20, 27 August 2006 (UTC)[reply]

54G12 Scattered spaces

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54G20 Counterexamples

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linas 15:51, 19 November 2006 (UTC)[reply]
Paul August ☎ 02:58, 27 August 2006 (UTC)[reply]
Paul August ☎ 01:54, 27 August 2006 (UTC)[reply]

54G99 Miscellaneous

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54Gxx Peculiar spaces

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54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)

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54H11 Topological groups

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54H12 Topological lattices, etc.

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54H13 Topological fields, rings, etc.

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54H15 Transformation groups and semigroups

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54H20 Topological dynamics

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54H25 Fixed-point and coincidence theorems

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54H99 Miscellaneous

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54Hxx Connections with other structures, applications

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