τ-metrizable spaces
Submitted: 2017-11-28
|Accepted: 2018-04-02
|Published: 2018-10-04
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Keywords:
τ-metric space, τ-metrizable space, τ-metrization theorem
Supporting agencies:
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.
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
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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.
