Talk:Comparison of topologies

Should we glue it with Weak topology?

Tosha 15:08, 22 Feb 2004 (UTC)

I think it is more useful to keep weak topology separate.

Charles Matthews 15:52, 22 Feb 2004 (UTC)

Article move and rewrite
Hasn't the rewrite made this harder to understand, for non-experts? Charles Matthews 14:02, 30 Apr 2005 (UTC)

Probably. On a another note: I was thinking that lattice of topologies would be a better name for this page. Comparison of topologies is a little vague. No one is going to search for comparison of topologies, whereas lattice of topologies can be found in the index of numerous topology books. I meant to move it awhile ago (when it was still at finer topology), but forgot. -- Fropuff 14:06, 2005 Apr 30 (UTC)


 * Hmmm - maybe a fresh page for that? Plenty of people need the 'finer'/'coarser' concepts. I can't say I have ever worried about the whole lattice of topologies; it's getting pretty abstract by that stage? Charles Matthews 14:41, 30 Apr 2005 (UTC)

My main aim (besides moving the article to Comparison of topologies) was to use the subset inclusion symbol ($$\subseteq$$) which I find very intuitive in this context, but my explanation was too brief. I had a second try. What do you think now ?

I copied the name comparison of topologies from the English translation of Bourbaki's topology book. Lattice of topologies is definitely better but perhaps a bit too abstract.MathMartin 14:44, 30 Apr 2005 (UTC)


 * By the way, the big Soviet encyclopedia calls this Comparison of topologies too. Charles Matthews 10:57, 27 May 2005 (UTC)

edited "Properties"
I switched "tau 1" and "tau 2" in the "Properties" section. Please verify that it is correct.

I was ecstatic when I found these mathematics pages. Thanks a million!

Lingji


 * Your edit made the statement correct. Thanks for fixing. MathMartin 07:23, 27 May 2005 (UTC)

Wrong sentence
The second sentence is wrong:

"A topology on a set may be defined as the collection of subsets which are considered to be "open". An alternative definition is that it is the collection of subsets which are considered "closed"."

The collection of closed sets of a topological space X is certainly an *equivalent* way to define the topology on X. But it is not an alternative definition.

The word "topology" always means the collection of open sets. Then if you want to define the topology on a set by means of the closed sets, that works fine.

But do not redefine the word "topology".2600:1700:E1C0:F340:C6E:324D:7979:1739 (talk) 23:00, 13 October 2018 (UTC)