Clones 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.

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...

$L$-Topological Spaces

‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness...

METACOMPACTNESS IN L-TOPOLOGICAL SPACES

In this paper the concept of metacompactness in L-topologicalspaces is introduced by means of point finite families of L-fuzzy sets. Thisfuzzy metacompactness is a natural generalization of Lowen fuzzy compactness.Further a characterization of fuzzy metacompactness in the weakly inducedL-topological spaces is also obtained.