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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:

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  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.
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  • If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
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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)[edit]

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[edit]

54B05 Subspaces[edit]

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[edit]

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

54B17 Adjunction spaces and similar constructions[edit]

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[edit]

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[edit]

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

54C25 Embedding[edit]

54C30 Real-valued functions[edit]

54C35 Function spaces[edit]

54C40 Algebraic properties of function spaces[edit]

54C45 $C$- and $C^*$-embedding[edit]

54C50 Special sets defined by functions[edit]

54C70 Entropy[edit]

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[edit]

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

54D70 Base properties[edit]

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[edit]

54E05 Proximity structures and generalizations[edit]

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

54E15 Uniform structures and generalizations[edit]

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[edit]

54E25 Semimetric spaces[edit]

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[edit]

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[edit]

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[edit]

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[edit]

54E99 Miscellaneous[edit]

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[edit]

54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces[edit]

54F45 Dimension theory[edit]

54F65 Topological characterizations of particular spaces[edit]

54F99 Miscellaneous[edit]

54Fxx Special properties[edit]

54G05 Extremally disconnected spaces, $F$-spaces, etc.[edit]

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

54G12 Scattered spaces[edit]

54G20 Counterexamples[edit]

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[edit]

54Gxx Peculiar spaces[edit]

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

54H11 Topological groups[edit]

54H12 Topological lattices, etc.[edit]

54H13 Topological fields, rings, etc.[edit]

54H15 Transformation groups and semigroups[edit]

54H20 Topological dynamics[edit]

54H25 Fixed-point and coincidence theorems[edit]

54H99 Miscellaneous[edit]

54Hxx Connections with other structures, applications[edit]

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