This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
-- "Every topological group is completely regular."
Teach me if I'm wrong, but I think this only holds for Hausdorff topological groups, maybe even only for locally compact groups. Since the wikipedia page for topological groups doesn't require hausdorff, this example should be removed (just in the case I'm right, for sure) -- Roman3 ( talk) 09:47, 12 July 2010 (UTC)
I corrected from
(This was introduced in http://en.wikipedia.org/?title=Tychonoff_space&diff=next&oldid=463867677 with saying clearer if the quantifiers are in the beginning. Yes, clearer but wrong in this case.) To
Carefully with correcting from ambiguous to unambiguous - do your hit the proper case? Best regards 90.180.192.165 ( talk) 21:10, 24 February 2012 (UTC)
The paragraph explaining the history of the concept in the lead is taken straight from Narici & Beckenstein. Now Narici & Beckenstein is a very fine book for functional analysis, but they are not historians. And in their historical commentaries they have the annoying habit of sometimes twisting the truth to get a better story. In this particular case, the notion of commpletely regular space was not introduced by Tychonoff. In fact, if you look at the 1930 paper from Tychonoff, Tychonoff himself mentions in a footnote that the notion was introduced in 1925 by Urysohn.
Please do not blindly reference N&B for historical stuff. They are not reliable for that.
Also, there is absolutely no need to spell out all the various transliterations of the name Tychonoff in this article. That belongs perfectly in the linked article Andrey Nikolayevich Tychonoff, but not here. PatrickR2 ( talk) 04:41, 22 October 2023 (UTC)
An example of a space that is a regular space but is not completely regular would be nice to have. I'm not seeing one, just right now. 67.198.37.16 ( talk) 23:11, 19 November 2023 (UTC)
The Tietze extension theorem can be applied to normal spaces to find a continuous real-valued function that separates two closed subsets. Apparently, this theorem won't work for regular spaces, because, if it did, then every regular space would automatically be completely regular. So why does this theorem break down for regular spaces? What is the insight, intuition for this? 67.198.37.16 ( talk) 23:24, 19 November 2023 (UTC)
The lede states that there are completely regular spaces that are not Hausdorff; and the first talk topic above suggests that this is often the case for topological groups. Can explicit examples be given? For example, by naming some topological group that is not Hausdorff? 67.198.37.16 ( talk) 23:36, 19 November 2023 (UTC)
It is mentioned that Tπ space is an alternative notation for Tychonoff spaces. This notation does not appear in any of the standard references. So at least it is not a notation in general use even if some author in the past may have used it once. Does anyone have a reference for this? PatrickR2 ( talk) 20:51, 3 December 2023 (UTC)
The article states "every topological group is completely regular". I had modified this to read "every commutative topological group is completely regular", but this was reverted, with a statement that "... even the non-commutative groups [are completely regular]" (See above.) Is there a reference for this? Perhaps this should be obvious? It's just not obvious to me. I don't have any particular intuition for this. Is there some way to think about this that would reveal the correctness of this statement? 67.198.37.16 ( talk) 00:50, 1 February 2024 (UTC)
This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
-- "Every topological group is completely regular."
Teach me if I'm wrong, but I think this only holds for Hausdorff topological groups, maybe even only for locally compact groups. Since the wikipedia page for topological groups doesn't require hausdorff, this example should be removed (just in the case I'm right, for sure) -- Roman3 ( talk) 09:47, 12 July 2010 (UTC)
I corrected from
(This was introduced in http://en.wikipedia.org/?title=Tychonoff_space&diff=next&oldid=463867677 with saying clearer if the quantifiers are in the beginning. Yes, clearer but wrong in this case.) To
Carefully with correcting from ambiguous to unambiguous - do your hit the proper case? Best regards 90.180.192.165 ( talk) 21:10, 24 February 2012 (UTC)
The paragraph explaining the history of the concept in the lead is taken straight from Narici & Beckenstein. Now Narici & Beckenstein is a very fine book for functional analysis, but they are not historians. And in their historical commentaries they have the annoying habit of sometimes twisting the truth to get a better story. In this particular case, the notion of commpletely regular space was not introduced by Tychonoff. In fact, if you look at the 1930 paper from Tychonoff, Tychonoff himself mentions in a footnote that the notion was introduced in 1925 by Urysohn.
Please do not blindly reference N&B for historical stuff. They are not reliable for that.
Also, there is absolutely no need to spell out all the various transliterations of the name Tychonoff in this article. That belongs perfectly in the linked article Andrey Nikolayevich Tychonoff, but not here. PatrickR2 ( talk) 04:41, 22 October 2023 (UTC)
An example of a space that is a regular space but is not completely regular would be nice to have. I'm not seeing one, just right now. 67.198.37.16 ( talk) 23:11, 19 November 2023 (UTC)
The Tietze extension theorem can be applied to normal spaces to find a continuous real-valued function that separates two closed subsets. Apparently, this theorem won't work for regular spaces, because, if it did, then every regular space would automatically be completely regular. So why does this theorem break down for regular spaces? What is the insight, intuition for this? 67.198.37.16 ( talk) 23:24, 19 November 2023 (UTC)
The lede states that there are completely regular spaces that are not Hausdorff; and the first talk topic above suggests that this is often the case for topological groups. Can explicit examples be given? For example, by naming some topological group that is not Hausdorff? 67.198.37.16 ( talk) 23:36, 19 November 2023 (UTC)
It is mentioned that Tπ space is an alternative notation for Tychonoff spaces. This notation does not appear in any of the standard references. So at least it is not a notation in general use even if some author in the past may have used it once. Does anyone have a reference for this? PatrickR2 ( talk) 20:51, 3 December 2023 (UTC)
The article states "every topological group is completely regular". I had modified this to read "every commutative topological group is completely regular", but this was reverted, with a statement that "... even the non-commutative groups [are completely regular]" (See above.) Is there a reference for this? Perhaps this should be obvious? It's just not obvious to me. I don't have any particular intuition for this. Is there some way to think about this that would reveal the correctness of this statement? 67.198.37.16 ( talk) 00:50, 1 February 2024 (UTC)