Dear Thomas, as far as I remember, Fourman & Grayson define and study separable locales toward the end of "Formal spaces". With best regards Giovanni Curi Quoting Thomas Streicher <streicher@mathematik.tu-darmstadt.de>:
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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