completely regular space

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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Let E be a Hausdorff topological vector space (so automatically a completely regular space), Y a topological vector space, and U an open subset of E.
Conversely, if (X, [tau]) is any completely regular space, then there exists a proximity [delta] on X such that [tau] = [tau]([delta])
In our result E will be a topological vector space so automatically a completely regular space. For convenience we state the result if E is a normal space and we remark on the general case after the theorem.
Let X be a Hausdorff completely regular space and A a subalgebra of C (X) which is either a [C.sub.b](X)-module or closed under the complex conjugation.
Let X be a Hausdorff completely regular space and A a subalgebra of C(X) which is either a [C.sub.b](X)-module or closed under the complex conjugation.
Let X be a Hausdor ff completely regular space, A [subset] C (X) a unitary algebra which is both a [C.sub.b](X)-module and closed under the complex conjugation.
Kubiak, Sandwich-type characterizations of completely regular spaces, Appl.
Arya, On almost normal and almost completely regular spaces, Glasnik Mat., 25(1970), 141-152.

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