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Spaces close to \({\mathbb{R}}^ n\). (English. Russian original) Zbl 0721.54034

Sib. Math. J. 31, No. 1, 181-183 (1990); translation from Sib. Mat. Zh. 31, No. 1(179), 214-216 (1990).
Only finite-dimensional locally compact metric spaces with a countable base are considered. By the theorem of Brouwer each n-dimensional closed subset F of \(R^ n\) has nonempty interior Int F, which also satisfies the following conditions: (a) Int F contains the cube \(I^ n\). (b) Int F contains a set V open in \(R^ n\) and homeomorphic to \(R^ n\). - The author defines a class of spaces with a property similar to property (b), and with the help of this class, using a modification of property (a), he gives a characterization of the open sets of \(R^ n\).

MSC:

54F65 Topological characterizations of particular spaces
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References:

[1] Y. Sternfeld, ?Dimensional of subsets of product spaces,? Proc. Am. Math. Soc.,82, No. 3, 452-454 (1981). · Zbl 0477.54022 · doi:10.1090/S0002-9939-1981-0612738-X
[2] K. Kuratowski, Topology, Vol. 2, Academic Press, New York (1969).
[3] K. Borsuk, Theory of Retracts, Monograf. Mat., P.W.N., Warsaw (1967). · Zbl 0153.52905
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