Talk:Countably generated space
 | This article is rated Start-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
| |||||||||||
Borel sets?
[edit]The current version of the article says that
- All borel sets are countably generated.
I don't have a clue what this sentence should mean -- it is definitely not true in any topological space. --Kompik 17:53, 11 April 2007 (UTC)
- i thought Borel sets are countably generated. if "countably genrated" has several meanings, we should put them in the article. Anyway, we need some examples for "countably generated" stuff. Jackzhp 00:49, 17 May 2007 (UTC)
Tightness
[edit]A topological space is countably generated <=> it has countable tightness. Therefore the term countably tight space is used often as well. I am not quite sure, which term is used more frequently. The goole search "countably tight" "topological space" has less hits that "countably generated" "topological space", but the term countably generated is used for many other constructions that topological spaces, which is, indeed, the case for many of the results of this search. (As far as I remember, I have seen several papers using this term for topological spaces, if it would be necassary, I could try to find precise citations.)
(The definition of tightness can be found in most standard topological textbooks, or e.g. here[1], the section Cardinal functions. I wasn't able to find tightness in wikipedia. The only thing about cardinal functions in topology I found here: Topological_property#Cardinal_functions. The Polish wiki has an entire article pl:Funkcja_kardynalna devoted to cardinal functions (including the ones used in topology), perhaps it would not be bad idea to make something similar in English wiki. (I didn't find anything similar here.) --Kompik 17:53, 11 April 2007 (UTC)
External links modified
[edit]Hello fellow Wikipedians,
I have just modified one external link on Countably generated space. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
- Added archive https://web.archive.org/web/20040917084107/http://thales.doa.fmph.uniba.sk/density/pages/slides/sleziak/paper.pdf to http://thales.doa.fmph.uniba.sk/density/pages/slides/sleziak/paper.pdf
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).
- If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
- If you found an error with any archives or the URLs themselves, you can fix them with this tool.
Cheers.—InternetArchiveBot (Report bug) 17:30, 13 August 2017 (UTC)