Mitrofan Mihailovich Choban, E. Michael
Abstract
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The following result is obtained, and is then applied to give a new proof of a set-valued selection theorem: For every nonempty Tychonoff space Y there exists a Tychonoff space X with dim X = 0, a perfect map f : X → Y, and a paracompact S ⊂ X with dim S = 0, such that f(S) = Y and f ∣ S is open.
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The following result is obtained, and is then applied to give a new proof of a set-valued selection theorem: For every nonempty Tychonoff space Y there exists a Tychonoff space X with dim X = 0, a perfect map f : X → Y, and a paracompact S ⊂ X with dim S = 0, such that f(S) = Y and f ∣ S is open.
Key concepts: Tychonoff space, Paracompact space, Mathematics, Zero (linguistics), Regular space, Space (punctuation), Open set, Normal space