completely regular space


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completely regular space

[kəm′plēt·lē ¦reg·yə·lər ′spās]
(mathematics)
A topological space X where for every point x and neighborhood U of x there is a continuous function from X to [0,1] with f (x) = 1 and f (y) = 0, if y is not in U.
References in periodicals archive ?
Conversely, if (X, [tau]) is any completely regular space, then there exists a proximity [delta] on X such that [tau] = [tau]([delta])
Arya, On almost normal and almost completely regular spaces, Glasnik Mat.

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