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We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
We propose a method of generating different scale-free networks, which has several input parameters in order to adjust the structure, so that they can serve as a basis for computer simulation of real-world phenomena. The topological…
In this paper, we study some properties of $*-$open and $*-$closed subsets of a space. The collection of all $*-$open subsets of a space $X$ form a topology on $X$ which is denoted by $^{*}O(X)$. We investigate the relations between…
Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
We develop a new method leading the structure of finite subsets S and T of an abelian group with $|S+T|\le |S|+|T|$. We show also how to recover the known results in this area in a relatively short space.
We show Lie algebra versions of some results on homological finiteness properties of subdirect products of groups, including a version of the 1-2-3 Theorem.
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
Recent results concerning the relation of topology and low-lying fermion modes are summarized.
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
Let $G$ be a finite abelian group, and let $S$ be a sequence over $G$. Let $f(S)$ denote the number of elements in $G$ which can be expressed as the sum over a nonempty subsequence of $S$. In this paper, we determine all the sequences $S$…
In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological…
A zero-sum sequence over ${\mathbb Z}$ is a sequence with terms in ${\mathbb Z}$ that sum to $0$. It is called minimal if it does not contain a proper zero-sum subsequence. Consider a minimal zero-sum sequence over ${\mathbb Z}$ with…
This note concerns the topology of the connected components of the zero sets of monochromatic random waves on compact Riemannian manifolds without boundary. In [SW] it is shown that these are distributed according to a universal measure on…
We develop a method that we call \emph{omission of intervals}, for establishing topological properties of subsets of the real line based on their combinatorial structure. Using this method, we obtain conceptual proofs of the fundamental…
We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and…
The aim of this paper is to study the topological properties of some classes of subsemimodules endowed with a subbasis closed-set topology. We show that such spaces are $T_0$. When the semimodule is finitely generated, those spaces are…