τ-metrizable spaces

A.C. Megaritis

Abstract

In [1], A. A. Borubaev introduced the concept of τ-metric space, where τ is an arbitrary cardinal number. The class of τ-metric spaces as τ runs through the cardinal numbers contains all ordinary metric spaces (for τ = 1) and thus these spaces are a generalization of metric spaces. In this paper the notion of τ-metrizable space is considered.


Keywords

τ-metric space; τ-metrizable space; τ-metrization theorem

Subject classification

54A05; 54E35.

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References

A. A. Borubaev, On some generalizations of metric, normed, and unitary spaces, Topology and its Applications 201 (2016), 344-349. https://doi.org/10.1016/j.topol.2015.12.045

R. Engelking, General Topology, Sigma Series in Pure Mathematics, 6. Heldermann Verlag, Berlin, 1989.

J. R. Munkres, Topology: a first course, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975.

L. A. Steen and J. A. Jr. Seebach, Counterexamples in topology, Dover Publications, Inc., Mineola, NY, 1995.

S. Willard, General topology, Dover Publications, Inc., Mineola, NY, 2004.

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Universitat Politècnica de València

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