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Concepts in Vector Spaces with Convergence Structures

Published online by Cambridge University Press:  20 November 2018

G. F. C. De Bruyn
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Limit vector spaces ('limitierte Vektorräume') 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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 4 , October 1975 , pp. 499 - 502
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Fischer, H. R., Limesraume, Math. Ann. 137 (1959), 269–303.Google Scholar
2. Hogbe-Nlend, H., Théorie des homologies et applications (Lecture notes in Mathematics, 213), Springer-Verlag, Berlin-Heidelberg-New York, 1971.Google Scholar
3. Kent, D., Convergence functions and their related topologies, Fund. Math. 54 (1964), 125–133.Google Scholar
4. Waelbroeck, L., Etude spectrale des algèbres complètes, Mémoires de l’Académie Royale de Belgique, 1960.Google Scholar