"separable" is used also to mean T_2 Prof. Peter Johnstone wrote:
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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