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We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
We survey some results on toric topology.
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
Given a sequence converging to zero, we consider the set of numbers which are sums of (infinite, finite, or empty) subsequences. When the original sequence is not absolutely summable, the subsum set is an unbounded closed interval which…
In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six…
The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.
We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.
We survey results on the distribution of zeros of random polynomials and of random holomorphic sections of line bundles, especially for large classes of probability measures on the spaces of holomorphic sections. We provide furthermore some…
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.
Results about the structure of the set of Egyptian fractions on the line are extended to subsets of topological groups.
We survey different topologizations of the set $\mathcal{S}(G)$ of all closed subgroups of a topological group $G$ and demonstrate some applications in Topological Grous, Model Theory, Geometric Group Theory, Topological Dynamics.
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…
We announce conditions under which a given sequence of points on the complex plane is a subsequence of zeros of an entire function with weight restrictions on growth.
We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups.
We show that a zero-sum-free sequence of length $n$ over an abelian group spans at least $2n$ distinct subsequence sums, unless it possesses a rigid, easily-described structure.
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the…
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…