Compactifications, C(x) and Ring Epimorphisms
نویسندگان
چکیده
Given a topological space X, K(X) denotes the upper semi-lattice of its (Hausdorff) compactifications. Recent studies have asked when, for αX ∈ K(X), the restriction homomorphism ρ : C(αX) → C(X) is an epimorphism in the category of commutative rings. This article continues this study by examining the sub-semilattice, Kepi(X), of those compactifications where ρ is an epimorphism along with two of its subsets, and its complement Knepi(X). The role of Kz(X) ⊆ K(X) of those αX where X is z-embedded in αX, is also examined. The cases where X is a P space and, more particularly, where X is discrete, receive special attention.
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