On a characterization of finite dimensional real linear spaces |
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Authors: | Janusz Kaptur |
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Affiliation: | 1. Institute of Mathematics, Maria Curie-Sklodowska University, 20-031, Lublin, Poland
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Abstract: | LetX be a real linear space; if is a linear topology onX, let denote the class of all bounded with respect to subsets ofX. In this paper it is shown that the spaceX is algebraically finite dimensional if and only if the class of all convex, absorbing and radially bounded subsets ofX is included in the intersection of all , where runs the set of all linear topologies onX. |
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