Abstract
LetX be a real linear space; if Open image in new window is a linear topology onX, let Open image in new window denote the class of all bounded with respect to Open image in new window 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 Open image in new window , where Open image in new window runs the set of all linear topologies onX.
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