International Journal of Topology, Volume 2, Issue 3

This article proposes a unified concept of topological types of convergence for nets of multifunctions between topological spaces. Any kind of convergence is representable by a (2n + 2)-tuple, n = 0, 1, …, of two special functions u and l, suc...

The origin of glass formation has been one of the greatest mysteries of science. The first clues emerged in GexSe1-x glasses, where the bond-stretching and bond angle-bending constraints are countable, and it was found that the most favorable composi...

Though a convergence space is connected if and only if its topological modification is connected, connected subsets of a convergence space differ from those of its topological modification. We explore which subsets exhibit connectedness for the conve...

We introduce the notion of bornological approach nearness as a unified extension of various classical nearness structures. By redefining completeness within this framework, we establish a generalized version of the Niemytzki–Tychonoff theorem. Our re...

Graph theory models relationships by representing entities as vertices and their interactionsas edges. To handle directionality and multiple head–tail assignments, various extensions—directed, bidirected, and multidirected graphs—ha...

Classical algebraic structures—such as magmas, groups, and Lie groups—are characterized by increasingly strong requirements in binary operation, ranging from no additional constraints to associativity, identity, inverses, and smooth-manif...

Let Y be a smooth compact n-manifold. We studied smooth embeddings and immersions β:M→R×Y of compact n-manifolds M such that β(M) avoids some priory chosen closed poset Θ of tangent patterns to the fibers of the obvious pro...