Talk:Separation axiom

message: Note that an older version of this page existed at Separation axioms, but the page was completely redesigned for the move.
There is old talk at Talk:Separation axioms, but this is largely irrelevant to the new page, so I haven't moved it.
-- Toby 20:56 Aug 5, 2002 (PDT)
:I've moved and history merged it to line up with the history merge I did on the main article. Graham87 06:22, 31 July 2013 (UTC)
thread_title: Note about old talk

message: Fully normal does not imply regular.
On the other hand, for a Hausdorff space, full normality and paracompactness are equivalent.
Manta 21:51, 19 December 2006 (UTC)
thread_title: Error

message: I have a book "Topological Methods in Chemistry" by Merrifield and Simmons that discusses T1/2 spaces. By their definition, a space is a T1/2-space if each point of the space is either open or closed or both. This notion was used for a discussion of finite topologies. It is claimed that T1/2 spaces are truly intermediate between T0 and T1 spaces in the sense that all T1 spaces are T1/2 and all T1/2 spaces are T0 and there exist weaker topologies that do that satisfy the stronger. However this separation axiom is not reflected in this article. Jason Quinn 00:30, 2 June 2007 (UTC)
thread_title:  T<sub>1/2</sub> spaces? 

message: Domenicozambella, in an edit summary, wrote:
: I erased a sentence that does not make much (any?) sense.
I put the sentence back.  It makes sense to me, but I wrote it, so that doesn't mean much.  Can it be improved?  —Toby Bartels (talk) 19:11, 12 December 2010 (UTC)
thread_title:  Senseless sentence? 

message: I'm a little confused why these are the definitions on Wiki. Are these the commonly accepted ones? I feel like since Counterexamples in Topology is such a famous book, all the axioms should match that book to avoid confusion.  — Preceding unsigned comment added by 2601:646:C900:3210:9C20:C011:B89F:6786 (talk) 00:12, 21 May 2022 (UTC)
replies: text: If you think that common terminology is missing, go ahead and add it.  If you think some terminology should be removed, that too is possible; either be bold and remove it, or discuss it here first.  FWIW, despite some amount of exposure to topology, I haven't heard of Counterexamples in Topology.  —Quantling (talk | contribs) 22:01, 24 May 2022 (UTC)

text: Counterexamples in Topology is a great book, but unfortunately the terminology is no longer current. The definitions here (particularly T3 vs regular and T4 vs normal, but also completely Hausdorff vs Urysohn) are the ones commonly accepted today (at least in English), largely under the influence of the book by Willard (see the references).  There is some discussion of this at History of the separation axioms, but it's hard to source that, so it's not very complete. ―Toby Bartels (talk) 04:40, 10 October 2022 (UTC)

text: The definitions on the wiki are mostly the currently used ones.  Counterexamples in Topology was written in 1970 and some of its terminology is a little dated, incompatible with more modern usage.  See in particular History of the separation axioms for the rationale of the definitions used in Wikipedia.  I would also recommend Willard as a reference, as well as taking a look at https://topology.pi-base.org. PatrickR2 (talk) 04:43, 10 October 2022 (UTC)
thread_title:  Why these definitions? 

message: It seems that the beautiful diagram that indicates the relationships between the various axioms has a problem at the top.  Perfectly normal spaces are always completely regular, and hence R0 (see https://math.stackexchange.com/questions/4525139 for example).  So in the diagram PN should be paired up with T6 and not a separate node. PatrickR2 (talk) 04:47, 10 October 2022 (UTC)
thread_title:  Diagram of relationships between the axioms 

message: I personally encounter seldomly separation axioms stronger than Hausdorffness other than in the context of general topology. But still, such axioms are involved in some common facts listed as follows. The T numbers refer to the theorem number of the pi-base (only main theorems are listed).
· A σ-compact and locally compact Hausdorff space is T4 (T26).
· A T3 Lindelöf space is T4 (T30).
· A nontrivial connected T4 space has at least cardinality of continuum (T80 and T309).
· A linearly ordered space is T5 (T273).
· A metrizable space is T6 (T268). 129.104.241.193 (talk) 02:04, 1 June 2024 (UTC)
thread_title:  Major occurrence of strong separation axioms