Talk:Topological property

message: We already have a huge list of topological properties at Topological space#Classification of topological spaces. Perhaps we should move that list here instead. -- Fropuff 00:58, 2005 Mar 6 (UTC)
I think it should be moved here. topological space is too long anyway. Note that I also created uniform properties some time ago as a parallel page discussing properties for uniform spaces. So on this page only properties preserved by continuous functions should be discussed. MathMartin 12:01, 6 Mar 2005 (UTC)

message: Good, I agree, let's move it here. BTW, the first four properties you have on the list (open set, interior, neighborhood, and limit point) aren't really topological properties in the usual sense of the word. Topological properties are properties of spaces invariant under homeomorphism (okay, every topological space is open in itself, but that is rather tautological; or one could say that the set of open sets—the topology— is a topological property but again, that's pure tautology). -- Fropuff 17:05, 2005 Mar 6 (UTC)
:Wittgenstein said all mathematics is tautology, and I share his opinion. If the homeomorphism maps the space onto itself and the topology is defined using the closure operator it is not tautological (at least not in my opinion) that open sets stay open under the homeomorphism. Or consider someone who does not know the definition of continuity in terms of open sets and is just looking for the properties studied in topology to get a feeling for the subject. My point is properties which you consider tautological might be suprising for someone else, depending on the direction he is coming from. Of course a balance has to be reached and it would certainly be overkill to explain why open sets are topological properties, but a short link certainly makes the article easier to understand. 
:If the article grows longer we can always put the tautological topological properties in a section called ==Basic properties==.
MathMartin 17:30, 6 Mar 2005 (UTC)
replies: text: Ok perhaps it should be explained better. I meant to say a homemorphism maps open sets to open sets. I can agree that this is a basic property of a topological space but I do not think it is strange to include it here. Perhaps someone else can give his opinion. MathMartin 18:03, 6 Mar 2005 (UTC)

text: I do not understand. Can you provide more details ? MathMartin 18:32, 3 October 2005 (UTC)

text: Thanks for the explanation, but I still do not understand. If you have a homeomorphism from a single point subspace U of Y to A then you have to consider the subspace topology on U induced by Y in which U is open (and closed). MathMartin 19:20, 3 October 2005 (UTC)
thread_title: Is open set a topological property

message: The entry for 'sober' mentions an 'irreducible' space
a search of 'irreducible' redirects to the hyperconnected space
I also found:
http://www.mathreference.com/top-dim,intro.html
are they the same thing (in the context of 'sober space') and if so,
should the first mention be wkfied to point at 'hyperconnected' and/or
an explanatory phrase inserted indicating theyr'e the same thing since
that's the first mention?
Thanks!
Zero sharp 22:13, 9 August 2007 (UTC)
thread_title: irreducible =? hyperconnected

message: I wonder, why homotopy groups and all kind of (co)homological invariants are not mention here.
Boris Tsirelson (talk) 09:07, 2 August 2008 (UTC)
thread_title: What about homology?