A neighborhood treatment of general topological spaces

Smooth Neighborhood Structures in a Smooth Topological Spaces

Abstract: Problem Statement: Various concepts related to a smooth topological spaces have been introduced and relations among them studied by several authors (Chattopadhyay, Ramadan, etc). Conclusion/Recommendations: In this study, we presented the notions of three sorts of neighborhood structures of a smooth topological spaces and give some of their properties which are results by Ying extende...

REDUNDANCY OF MULTISET TOPOLOGICAL SPACES

In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^star(U),sqsubseteq)$ and $(Ds(varphi(U)),subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.

Topological Interpretation of Function Spaces Stable under a General Operation

Function (linear) spaces E on which some arbitrary real or complex continuous function operates (in other words, E is stable under the unary operation defined by this function) were studied by K. de Leeuw, Y. Katznelson, Y. Sternfeld and Y. Weit, showing, e.g. that for a complex function space E consisting of bounded functions, containing the constants and closed w.r.t. the sup-norm, if some no...

A note on soft topological spaces

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 ...

σ-Normality of Topological Spaces