Related papers: Some observations on filters with properties defin…
In this paper we consider some recent relative versions of Menger property called set strongly star Menger and set star Menger properties and the corresponding Hurewicz-type properties. In particular, using \cite {BMae}, we "easily" prove…
We study some topological properties of attractors.
In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact…
In this paper, we continue to investigate topological properties of $\mathcal{I}H$ and its two star versions namely $SS \mathcal{I} H$ and $S \mathcal{I} H$. We characterized $\mathcal{I}$-Hurewicz property by $\mathcal{I}$-Hurewicz Basis…
If $\mathcal P$ is a family of filters over some set $I$, a topological space $X$ is \emph{sequencewise $\mathcal P$-\brfrt compact} if, for every $I$-indexed sequence of elements of $X$, there is $F \in \mathcal P$ such that the sequence…
The main goal of this paper is to investigate relations between topologies obtained by: $\theta$-open sets, $\omega$-open sets, $\theta_\omega$-open sets, local function, and local closure function with ideal of the countable sets. As the…
In the present survey paper, we present several new classes of Hochster's spectral spaces "occurring in nature", actually in multiplicative ideal theory, and not linked to or realized in an explicit way by prime spectra of rings. The…
We characterize exactly the compactness properties of the product of \kappa\ copies of the space \omega\ with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard…
This article is a continuation of the study of bornological open covers and related selection principles in metric spaces done in (Chandra et al. 2020) using the idea of strong uniform convergence (Beer and Levi, 2009) on bornology. Here we…
A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the development of schemes for parallel computation and compression…
The rings of linear continuous operators on the topological spaces of $\mathfrak{G}$-zero maps were described, where $\mathfrak{G}$ is a filter on a set with an involution. This applies to modules of formal series with well ordered support…
Algebraic properties of $n$-place opening operations on a fixed set are described. Conditions under which a Menger algebra of rank $n$ can be represented by $n$-place opening operations are found.
We use convergence theory as the framework for studying H-closed spaces and H-sets in topological spaces. From this viewpoint, it becomes clear that the property of being H-closed and the property of being an H-set in a topological space…
In this paper we construct consistent examples of subgroups of $2^\omega$ with Menger remainders which fail to have other stronger combinatorial covering properties. This answers several open questions asked by Bella, Tokgoz and Zdomskyy…
This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.
First of all, we focused soft {\beta}-open sets and soft {\beta}-closed sets over the soft topological space and investigated some properties of them. Secondly, we defined the concepts soft {\beta}-continuity, soft {\beta}-irresolute and…
A class of Cantor-type spaces and related geometric structures are discussed.
Let $K$ be a field and let $A$ be a subring of $K$. We consider properties and applications of a compact, Hausdorff topology called the "ultrafilter topology" defined on the space Zar$(K|A)$ of all valuation domains having $K$ as quotient…
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…
We first introduce and investigate a new class of $T_0$ spaces -- strong R-spaces, which are stronger than both R-spaces and strongly well-filtered spaces. It is proved that any sup-complete poset equipped with the upper topology is a…