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Concepts in vector spaces with convergence structures

1975
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Canadian mathematical bulletin
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1. Introduction. Limit vector spaces (iimitierte Vektorraume') were defined by Fischer [1] and concepts such as continuity, compactness, etc. were introduced and studied by him and others, e.g. by Kent [3]. In this paper the concepts of precompactness and boundedness in limit vector spaces are studied. It is shown that most of their properties in topological vector spaces hold in limit vector spaces. The notions of 'espaces à bornés' (tfè-spaces) and 'espaces à bornés complets' (tfèc-spaces)

doi:10.4153/cmb-1975-091-3
fatcat:qysk5awjlzgabeyrjevb6dihku