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Question: 615 theorem let xt be a topological space and let...

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6.15 Theorem: Let (X,T) be a topological space and let S be a subbase for (X,T). The space (X.,T) is completely regular space if and only if for (X,T). The space (X,T) is completely regular space if and only if for every a e X and every V E S with a E V, there exists a contimous function f : X-1 such that f(a) = 0 and f(y) = 1, y EX\V. PROOF: exercise

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