Talk:Countably generated space

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)

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 [http://scholar.google.com/scholar?q=%22countably+tight%22+%22topological+space%22 "countably tight" "topological space"] has less hits that

[http://scholar.google.com/scholar?q=%22countably+generated%22+%22topological+space%22 "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[http://math.berkeley.edu/~apollo/topodefs.ps], 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)

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