On axioms of convergence in linear spaces

Andrzej Kamiński

Published: 1985-09-30

Vol. 1 (1985)

On axioms of convergence in linear spaces

Andrzej Kamiński

Abstract

By a (general) convergence in a given linear space X we mean a mapping G: X^N→2^X, where N denotes the set of all positive integers, and by a zero-convergence in X we mean a convergence G₀ in X for which G₀(x)≠⌀ implies 0∈G₀(x) for each x∈X^N. In the paper, the two operations are defined: 1° operation C, which to each zero-convergence G₀ in X assigns some general convergence G in X, and 2° operation C₀, which to each general convergence G in X assigns a zero-convergence G₀ in X. Various systems of axioms for general convergences and zero-convergences are considered and their connections with the operations C and C₀ are studied. Also mutual independence of axioms is studied.

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Kamiński, A. (1985). On axioms of convergence in linear spaces. Annales Mathematicae Silesianae, 1, 130–144. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14344

References

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Vol. 1 (1985)
Published: 1985-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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