Topological aspects of Poset spaces

Topological Aspects of Poset Spaces

We study two classes of spaces whose points are filters on partially ordered sets. Points in MF spaces are maximal filters, while points in UF spaces are unbounded filters. We give a thorough account of the topological properties of these spaces. We obtain a complete characterization of the class of countably based MF spaces: they are precisely the second-countable T1 spaces with the strong Cho...

Poset models of topological spaces

We consider poset models of topological spaces and show that every T1-space has an bounded complete algebraic poset model, thus give a positive answer to a question asked in a recent paper by Waszkiewicz. It is also proved that every T1-space is homeomorphic to the maximal point space of a d-space. In the classic general topology, people are mainly interested in the spaces which satisfy at leas...

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...