Separation axioms and covering dimension of asymmetric normed spaces

Separation in General Normed Vector Spaces

The goal here is to extend this result to general normed vector spaces over the reals. Informally, a “vector space over the reals,” is a set X together with the operations vector addition and scalar multiplication, which are assumed to have the usual properties (e.g., vector addition is commutative). “Over the reals” means that scalars are in R rather than in some other field, such as the compl...

Higher Separation Axioms in Generalized Closure Spaces

The hierarchy of separation axioms that is familiar from topological spaces generalizes to spaces with an isotone and expansive closure function. Neither additivity nor idempotence of the closure function must be assumed.

Separation axioms in fuzzy bitopological spaces

In this paper, we give and study different types of separation axioms using the remoted neighbourhood of a fuzzy point and a fuzzy set in the fuzzy supratopological Spaces (X, s τ ) which is generated by the fuzzy bitopological space (X, 1 2 , τ τ ). Several properties on these separation axioms are researched.

BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

On bD-Sets and Associated Separation Axioms