Epireflections in the category of $T_0$-spaces

L. Nel; R. Wilson

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$𝐒𝐩𝐅𝐢$ is the category of spaces with filters: an object is a pair $(X, ℱ)$ , $X$ a compact Hausdorff space and $ℱ$ a filter of dense open subsets of $X$ . A morphism $f (Y, 𝒢) \to (X, ℱ)$ is a continuous function $f Y \to X$ for which $f^{- 1} (F) \in 𝒢$ whenever $F \in ℱ$ . This category arises naturally from considerations in ordered algebra, e.g., Boolean algebra, lattice-ordered groups and rings, and from considerations in general topology, e.g., the theory of the absolute and other covers, locales, and frames, though we shall specifically...

Displaying similar documents to “Epireflections in the category of T 0 -spaces”

Displaying similar documents to “Epireflections in the category of $T_{0}$ -spaces”