On the topological linear spaces whose subspace lattices are modular |
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Authors: | Jan Hamhalter |
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Institution: | 1. Electrical Engineering, Department of Mathematics, Technical University of Prague, Technická 2, 166 27, Prague 6, Czechoslovakia
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Abstract: | LetX be a topological linear space and letL(X) be a lattice of all closed subspaces ofX. We show that in many cases the modularity ofL(X) implies that every bounded subset ofX is finite-dimensional. We derive some topological consequences of the latter result. Due to the significance of the modularity condition forL(X) in quantum axiomatics and elswhere (see 1,14,15]) results also might find application outside the realm of topological linear spaces. |
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