NOTES ON EQUICONTINUITY IN TOPOLOGICAL VECTOR SPACES
Keywords:
equicontinuous set of linear maps (functionals), Null netAbstract
Equicontinuity is a Uniform Space (General Topology (GT)) concept that has
assumed some notoriety in Locally Convex Space theory (Topological Vector Spaces
(TVS)). We here
(i) Trace the link from GT to TVS, and
(ii) Exploit the link to assemble some notes.
In addition, from the notes, we show that:
(iii) The T-limited sets of John Webb are equicontinous sets of linear functionals. [7].
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References
Sunday Oluyemi, Net (Sequential) Characterization of Equicontinuity, Trans. of NAMP, Vol. 17, 17-24 (2021).
John Hornvath, Topological Vector Spaces and Distributions I, Addison Wesly, 1966.
Albert Wilansky, Modern Methods in Topological Vector Spaces, McGrawHill, 1976.
Sterling K. Berberian, Lectures in Functional Analysis and Operator Theory, GTM 15, Sopringer-Verlag, World Publishing Corporation, Beijin, China, 1974.
Warren Page, Topological Uniform Structures, Dover Publications Inc., New York, 1981.
Sunday Oluyemi, The pseudometric topology of a seminorm is a vector topology, Transanctions of NAMP, Volume 12, July – September 2020 Issue Pp. 1 – 10.
John H. Webb, Sequential converg3ence in locally convex spaces, Proceedings Cambridge Philosophical Society, 64(1968), 341 – 369.
Sunday Oluyemi, A vector topology is uniformizable, Journal of NAMP, Volume 60, April – June, 2021, Issue, p.1 – 4.
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