Strongly Far Proximity and Hyperspace Topology

Year 2020, Volume: 1 Issue: 1, 23 - 29, 31.01.2020

James F. Peters , Clara Guadagni

Abstract

This paper introduces strongly far in proximity spaces.
Usually, when we talk about proximities, we mean \textit{Efremovi\v{c} proximities}. Nearness expressions are very useful and also represent a powerful tool because of the relation existing among \textit{Efremovi\v c proximities}, \textit{Weil uniformities} and $\mbox{T}_2$ compactifications. But sometimes \textit{Efremovi\v c proximities} are too strong. So we want to distinguish between a weaker and a stronger forms of proximity. For this reason, we consider at first \textit{Lodato proximity} $\delta$ and then, by this, we define a stronger proximity by using the Efremovi\v{c} property related to proximity.

Keywords

Hit-and-miss topology, Hyperspaces, Proximity, Strongly far

Supporting Institution

Natural Sciences \& Engineering Research Council of Canada (NSERC)

Project Number

185986

Thanks

Many thanks for the invitation to submit this paper.

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