A note on soft topological spaces

Document Type: Research Paper

Authors

1 School of Mathematics and Statistics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, 100081 Beijing, P.R. China

2 School of Mathematics and Statistics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, 100081 Beijing, P. R. China

Abstract

This paper demonstrates the redundancies concerning the increasing popular ``soft set" approaches to general topologies. It is shown that there is a complement preserving isomorphism (preserving arbitrary $widetilde{bigcup}$ and arbitrary $widetilde{bigcap}$) between the lattice ($mathcal{ST}_E(X,E),widetilde{subset}$) of all soft sets on $X$ with the whole parameter set $E$ as domains and the powerset lattice ($mathcal{P}(Xtimes E),subseteq$) of all subsets of $Xtimes E$. It therefore follows that soft topologies are redundant and unnecessarily complicated in theoretical sense.

Keywords


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