Related papers: Soft Bitopological Spaces via Soft Elements
In this paper, it is shown that a topological space $X$ is compact iff every maximal ideal of the power set ring $\mathcal{P}(X)$ converges to exactly one point of $X$. Then as an application, simple and ring-theoretic proofs are provided…
It is a well-known result in pointfree topology that every locally compact frame is spatial. Whether this result extends to MT-algebras (McKinsey-Tarski algebras) was an open problem. We resolve it in the negative by constructing a locally…
We give a definition of compactness in L-fuzzy topological spaces and provide a characterization of compact L-fuzzy topological spaces, where L is a complete quasi-monoidal lattice with some additional structures, and we present a version…
We introduce the strong Gelfand-Phillips property for locally convex spaces and give several characterizations of this property. We characterize the strong Gelfand-Phillips property among locally convex spaces admitting a stronger Banach…
In this paper, the concept of neutrosophic soft filter and its basic properties are introduced. Later, we set up a neutrosophic soft topology with the help of a neutrosophic soft filter. We also give the notions of the greatest lower bound…
We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…
The central idea of metamaterials and metaoptics is that, besides their base materials, the geometry of structures offers a broad extra dimension to explore for exotic functionalities. Here, we discover that the topology of structures…
Topological defects are singularities within a field that cannot be removed by continuous transformations. The definition of these irregularities requires an ordered reference configuration, calling into question whether they exist in…
We prove an "abelian, locally compact" Whitehead theorem in fine shape: A fine shape morphism between locally connected finite-dimensional locally compact separable metrizable spaces with trivial $\pi_0$ and $\pi_1$ is a fine shape…
The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other…
Basic pairs and their morphisms are the most elementary framework in which standard topological notions can be defined. We present here a new interpretation of topological concepts as those which can be communicated faithfully between the…
The following selection theorem is established:\\ Let $X$ be a compactum possessing a binary normal subbase $\mathcal S$ for its closed subsets. Then every set-valued $\mathcal S$-continuous map $\Phi\colon Z\to X$ with closed $\mathcal…
This chapter develops the concept of \textbf{meekly $SC^*$-normality}, a novel generalization of the classical notion of normality in topology. The proposed framework simultaneously broadens $SC^*$-normality and other established forms of…
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…
We investigate $\mathcal F$-Borel topological spaces. We focus on finding out how a~complexity of a~space depends on where the~space is embedded. Of a~particular interest is the~problem of determining whether a~complexity of given space $X$…
A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory --…
For every finite closure space $X$ one can define a finite topological space $\operatorname{Top} X$ together with a natural projection $\operatorname{Top} X\longrightarrow X$. This could allow to apply the techniques of topological…
Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of…
For a collection of subcategories satisfying a fixed set of conditions, for example thick subcategories of a triangulated category, we define a topological space called classifying space of subcategories. We show that this space classifies…
We introduce the set-self-Tietze property, an analogue of the self-Tietze property for upper semi-continuous set-valued functions. A topological space $X$ is self-Tietze, if for every closed $A \subseteq X$ and continuous function $f \colon…