An Operational Characterization of Soft Topologies by Crisp Topologies

An Operational Characterization of Soft Topologies by Crisp Topologies

This paper contributes to the expanding literature on soft topology. We first prove that soft topologies can be characterized by crisp topologies. This takes advantage of two connected constructions that produce soft topologies from crisp topologies and vice versa. Both constructions are explicit an...

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Bibliographic Details
Main Author: José Carlos R. Alcantud
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Mathematics
Subjects:
soft topology
topology
base for a topology
second-countable space
separability
Online Access:https://www.mdpi.com/2227-7390/9/14/1656
Description
Summary:This paper contributes to the expanding literature on soft topology. We first prove that soft topologies can be characterized by crisp topologies. This takes advantage of two connected constructions that produce soft topologies from crisp topologies and vice versa. Both constructions are explicit and amenable to mathematical manipulations. Various consequences demonstrate that our theory has far-reaching implications for the development of soft topology and its extensions.
ISSN:2227-7390

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