In this article we established the concept of multi-continuity in minimal structure spaces (in short $\mathscr{M}$ space) and notion product space multiset topological space. Continuity between $\mathscr{M}$-space, generalized topology ideal spaces. We have investigated some basic properties $\mathscr{M}$–continuity space, such as composition $\mathscr{M}$–continuous functions, functions etc.

According to the definition of quasiweak almost periodic point, we introduce QWG(f) in paper. We studied topological structure G-quasiweak point set. have following two results: (1) Let (Y,d′) be a compact G–metric space and f : X → equicontinuous. {fn}∞n=1 G-strongly uniform converge map xk ∈ QWG(fn). If limk ∞ = x, then x QWG(f); (2) G-metric is f, lim sup QWG(fn) ⊂ QWG(f). The conclusions re...

Recent studies have shown that basic steric and connectivity constraints encoded at the secondary structure level are key determinants of 3D structure and dynamics in simple two-way RNA junctions. However, the role of these topological constraints in higher order RNA junctions remains poorly understood. Here, we use a specialized coarse-grained molecular dynamics model to directly probe the the...

Lovász invoked topological colouring bounds in proving Kneser’s Conjecture. Subsequently, numerous applications of topological techniques to graph colouring problems have arisen. However, even today, little is known about how to construct a graph with a particular topological colouring bound, or about the structure of such graphs. The aim of this thesis is to remedy this deficit. First, we will...

A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all maps of groupoid structure are continuous. The notion of monodromy groupoid of a topological groupoid generalizes those of fundamental groupoid and universal cover. It was earlier proved that the monodromy groupoid o...

This study focuses on the topology optimization of structures using a hybrid of level set method (LSM) incorporating sensitivity analysis and isogeometric analysis (IGA). First, the topology optimization problem is formulated using the LSM based on the shape gradient. The shape gradient easily handles boundary propagation with topological changes. In the LSM, the topological gradient method as ...

In this paper by considering a fuzzy continuous action of a fuzzy topological group on a fuzzy topological space we have fuzzifiifed the notion of topological dynamical system. Some properties of this fuzzy structure are investigated. Then we have constructed mixed fuzzy topological dynamical system from two given fuzzy topological dynamical systems.

In this paper we consider the problem of converting a large database of 2D polygons into a topological data structure (a data structure with nodes, edges and faces). We present EDGECRACK, an algorithm to obtain the topological data structure (which is based on a known algorithm for segment intersection) and performs small geometric corrections of the input by snapping to avoid problems. We furt...

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...