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\(\alpha\) r-spaces and some of their properties. (English) Zbl 0597.54002
Summary: In ibid. 33, 249-256 (1983; Zbl 0533.54001) the author has introduced the notion of an r-space and has shown that topological spaces are special cases of r-spaces. It is well known that if X is a topological space, then (1) the closure of the union of two subsets of X is the union of their closures. In the present paper we study r-spaces satisfying properties analogous to (1) for some subsets of X and give some conditions for a decomposition of such r-spaces into topological spaces.
MSC:
54A05 Topological spaces and generalizations (closure spaces, etc.)
Keywords:
r-spaces
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References:
[1] KELLEY J. L.: General Topology. D. VAN NOSTRAND COMPANY, New York 1955. · Zbl 0066.16604
[2] ZUZČÁK I.: Generalized topological spaces. Math. Slovaca) · Zbl 0533.54001
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