Sequential Convergence in Topological Vector Spaces

A. K. Katsaras; V. Benekas

doi:10.1515/gmj.1995.151

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Sequential Convergence in Topological Vector Spaces

A. K. Katsaras V. Benekas

Year: 1995 Journal: Georgian Mathematical Journal Vol: 2 (2)Pages: 151-164 Publisher: Springer Science+Business Media

DOI: 10.1515/gmj.1995.151

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Abstract

Abstract For a given linear topology τ , on a vector space E , the finest linear topology having the same τ convergent sequences, and the finest linear topology on E having the same τ precompact sets, are investigated. Also, the sequentially bornological spaces and the sequentially barreled spaces are introduced and some of their properties are studied.

Keywords:

Mathematics Topology (electrical circuits) Topological vector space Topological space Locally convex topological vector space Convergence (economics) Weak topology (polar topology) General topology Vector space Normed vector space Dual space Extension topology Pure mathematics Combinatorics

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Fuzzy and Soft Set Theory

Social Sciences → Decision Sciences → Management Science and Operations Research

Approximation Theory and Sequence Spaces

Physical Sciences → Mathematics → Statistics and Probability

Sequential Convergence in Topological Vector Spaces

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