Josef Ondřej

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seen Apr 19 '13 at 16:43

Feb
12
comment $X$ metric separable then $C(X)$ separable
@Martin: Aaaa, that explains it. Thanks very much. So in the case when X is compact, the proposition holds. I found it prooved also in a book by R. M. Dudley, but the proof seemed a bit more complicated. To the second remark, I think on a compact space all continuous functions must be bounded so I guess it shouldn't be a problem there, but you were right I was missing that in the more general case. course.zjnu.cn/hnc/shibian/… - Corollary 11.2.5
Feb
12
accepted $X$ metric separable then $C(X)$ separable
Feb
12
comment $X$ metric separable then $C(X)$ separable
Thanks very much, I'm asking because I read answer to this question at.yorku.ca/cgi-bin/… and it seems to me that the compactness is used only to show that the base for X is countable, so separability of X should be sufficient to prove my original proposition (which you disproved), what am I missing?
Feb
12
asked $X$ metric separable then $C(X)$ separable
Nov
30
awarded  Scholar
Nov
30
accepted separable iff homeomorphic to totally bounded
Nov
29
comment separable iff homeomorphic to totally bounded
To Brian M. Scott: Separable => homeomorphic to a totally bounded space is causing trouble. To kahen: Isn't every totally bounded space separable? I'm not sure, but is it necessary to use the argument with completion?
Nov
29
awarded  Student
Nov
29
asked separable iff homeomorphic to totally bounded