The Stone-Čech compactification of Tychonoff spaces
نویسنده
چکیده
A topological space X is said to be completely regular if whenever F is a nonempty closed set and x ∈ X \F , there is a continuous function f : X → [0, 1] such that f(x) = 0 and f(F ) = {1}. A completely regular space need not be Hausdorff. For example, ifX is any set with more than one point, then the trivial topology, in which the only closed sets are ∅ and X, is vacuously completely regular, but not Hausdorff. A topological space is said to be a Tychonoff space if it is completely regular and Hausdorff.
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