In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to L-topological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived.

In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it further applied to fractional integral equations proving existence results solutions under mixed Lipschitz weakly sequentially continuous conditions. Finally, an example given illustrate result.

We show that every Abelian group satisfying a mild cardinal inequality admits a pseudocompact group topology from which all countable subgroups inherit the maximal totally bounded topology (we say that such a topology satisfies property ♯). This criterion is used in conjunction with an analysis of the algebraic structure of pseudocompact groups to obtain, under the Generalized Continuum Hypothe...

We investigate the topology of complete Riemannian manifolds with the radial curvature at the base manifold bounded below by those of model surfaces. Here, model surfaces are generalized surfaces of revolution and warped product models which are diffeomorphic to S.

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

Abstract. The purpose of this note is to complete the study, begun in the first author’s PhD thesis, of the topology of the poset of generalized noncrossing partitions associated to real reflection groups. In particular, we calculate the Euler characteristic of this poset with the maximal and minimal elements deleted. As we show, the result on the Euler characteristic extends to generalized non...

In this article, we study two open problems posed by Edelman & Reiner about topology of certain simplicial complexes associated with abstract convex geometries. As a special case, we concentrate on generalized convex shellings, which were introduced by Kashiwabara, Nakamura & Okamoto for their representation theorem of abstract convex geometries. We answer one of the problems affirmatively for ...

The generalized de Bruijn digraph GB(n,d) has good properties as an interconnection network topology. The resource location problem in an interconnection network is one of the facility location problems. Finding absorbants of a digraph corresponds to solving a kind of resource location problem. In this paper, we solve some open problems given in the article ”Erfang Shan, T.C.E.Cheng, Liying Kan...