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Wikipedia:WikiProject Mathematics/PlanetMath Exchange/54-XX General topology

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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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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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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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