Chatyrko, V. A. 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 \(R^ n\). Reviewer: S.Gacsályi (Debrecen) MSC: 54F65 Topological characterizations of particular spaces Keywords:Euclidean spaces; Brouwer space PDFBibTeX XMLCite \textit{V. A. Chatyrko}, Sib. Math. J. 31, No. 1, 181--183 (1990; Zbl 0721.54034); translation from Sib. Mat. Zh. 31, No. 1(179), 214--216 (1990) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.