The Completion of Topological Spaces

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.

On the Topological Completion

Let A be a Tychonoff space. As is well known, the points of the Stone-Cech compactification ßX "are" the zero-set ultrafilters of X, and the points of the Hewitt real-compactification vX are the zero-set ultrafilters which are closed under countable intersection. It is shown here that a zeroset ultrafilter is a point of the Dieudonné topological completion SX iff the family of complementary coz...

σ-Normality of Topological Spaces

s-Topological vector spaces

In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...

On the topological equivalence of some generalized metric spaces

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...