A NOTE ON SPACES VIA DENSE SETS

Dense Sets on Bigeneralized Topological Spaces

The purpose of this paper is to introduce the concept and some fundamental properties of dense sets on bigeneralized topological spaces.

A Note on Naturally Ordered Sets in Semi-metric Spaces

A note on self-extremal sets in Lp(Ω) spaces

We give a necessary condition for a set in Lp(Ω) spaces (1 < p <∞) to be self-extremal that partially extends our previous results to the case of Lp spaces. Examples of self-extremal sets in Lp(Ω) (1 < p <∞) are also given. In [4, 5], we introduced the notion of (self-) extremal sets of a Banach space (X ,‖ · ‖). For a nonempty bounded subset A of X , we denote by d(A) its diameter and by r(A) ...

A Note on Αcozero-complemented Spaces and Αborel Sets

α is a regular cardinal number or the symbol ∞, and X is a compact Hausdorff space. It is shown that (Theorem 2.1) X is αcozerocomplemented iff each αBorel set differs from an αcozero set by a meagre set. This immediately yields (Corollary 2.2) X is αdisconnected iff each αBorel set differs from a clopen set by a meagre set. (The cases α = ∞ in Theorem 2.1, and α = ω1 in Corollary 2.2 are impor...

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 ...