Considering the increasing interest in fuzzy theory and possible applications, the concept of fuzzy metric space concept has been introduced by several authors from different perspectives. This paper interprets the theory in terms of metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology. We study interrelationships between this theory and other fuzzy theories such as intuit...

We extend Stone duality between generalized Boolean algebras and Boolean spaces, which are the zero-dimensional locally-compact Hausdorff spaces, to a non-commutative setting. We first show that the category of right-handed skew Boolean algebras with intersections is dual to the category of surjective étale maps between Boolean spaces. We then extend the duality to skew Boolean algebras with in...

We continue to study one of the classic problems in general topology raised by P. S. Alexandrov: when a Hausdorff space X has continuous bijection (a condensation) onto compactum? concentrate on situation not only but also $$X\setminus Y$$ can be condensed compactum whenever cardinality Y does exceed certain $$\tau$$ .

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

We bound the nuclear dimension of crossed products associated to some partial actions finite groups or Z on dimensional locally compact Hausdorff second countable spaces. Our results apply globalizable actions, group minimal automorphisms, and automorphisms acting zero-dimensional spaces, a class one containing 1-dimensional CW complexes. This extends work global systems by Hirshberg Wu.

The existence of coincidence and fixed points for continuous mappings in compact Hausdorff spaces is established. Some equivalent conditions of the existence of fixed and common fixed points for any continuous mapping and a pair of mappings in compact Hausdorff spaces are given, respectively. Our results extend, improve, and unify the corresponding results due to Jungck, Liu, and Singh and Rao.