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From: "Prof. Peter Johnstone"
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Subject: Re: separable locale
Date: Sun, 5 Jul 2009 21:54:50 +0100 (BST)
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Dear Thomas,
I'm pretty sure that what Michael meant by "separable" was what
most topologists would call "second countable" -- i.e., countably
generated as a frame. (There are some topology textbooks in which
this condition is called "completely separable".)
Peter Johnstone
---------------------------------
On Tue, 30 Jun 2009, Thomas Streicher wrote:
> Recently rereading Fourman's "Continuous Truth" I came across the term
> "separable locale" but could nowhere find an explanation. Does it mean a
> cHa A for which there exists a countable subset B such that ever a in A is
> the supremum of those b in B with b leq a. This would be the point free
> account of "second countable", i.e. having a countable basis.
> Of course, second countable T_) spaces are separable, i.e. have a
> countable
> dense set.
> Is this reading the "usual" one?
>
> Thomas
>
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