Sublocales in formal topology
نویسندگان
چکیده
منابع مشابه
Sublocales in formal topology
The paper studies how the localic notion of sublocale transfers to formal topology. For any formal topology (not necessarily with positivity predicate) we define a sublocale to be a cover relation that includes that of the formal topology. The family of sublocales has set-indexed joins. For each set of base elements there are corresponding open and closed sublocales, boolean complements of each...
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This paper investigates aspects of measure and randomness in the context of locale theory (point-free topology). We prove that every measure (σ-continuous valuation) μ, on the σ-frame of opens of a fitted σ-locale X, extends to a measure on the lattice of all σ-sublocales of X (Theorem 1). Furthermore, when μ is a finite measure with μ(X) = M , the σ-locale X has a smallest σ-sublocale of measu...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2007
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1185803619