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A dual analogue of spaces that are \(\Phi G_{\delta}\)-closed in the Smirnov compactification. (English. Russian original) Zbl 0571.54019

Russ. Math. Surv. 40, No. 1, 207-208 (1985); translation from Usp. Mat. Nauk 40, No. 1(241), 183-184 (1985).
The author introduces the following property of a space \(X\). Let \({\mathcal M}\) be a family of nonempty compact subsets of \(X\). Then \(X\) is said to be of countable type with respect to \({\mathcal M}\) if each \(M\in {\mathcal M}\) is contained in a compact set of countable character in \(X\). The author gives various characterizations of the property that yield, in particular, new characterizations of spaces of countable type and spaces of point countable type. Moreover, the property is extended to proximity spaces via Smirnov compactifications.
Reviewer: R.Telgársky

MSC:

54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54E05 Proximity structures and generalizations
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