Related papers: A combinatorial approach to certain topological sp…

Let S be a compact oriented surface. A homology cobordism of S is a cobordism C between two copies of S, such that both the "top" inclusion and the "bottom" inclusion of S in C induce isomorphisms in homology. Homology cobordisms of S form…

In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of $n$ definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the…

Here we classify all topological spaces where all bijections to itself are homeomorphisms. As a consequence, we also classify all topological spaces where all maps to itself are continuous. Analogously, we classify all measurable spaces…

The aim of this paper is to introduce the concepts of homotopical smallness and closeness. These are the properties of homotopical classes of maps that are related to recent developments in homotopy theory and to the construction of…

The aim of this paper is to continue the study of sg-compact spaces, a topological notion much stronger than hereditary compactness. We investigate the relations between sg-compact and $C_2$-spaces and the interrelations to hereditarily…

A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…

We define combinatorial analogues of stable and unstable minimal surfaces in the setting of weighted pseudomanifolds. We prove that, under mild conditions, such combinatorial minimal surfaces always exist. We use a technique, adapted from…

A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…

In this paper, we introduce and study the concepts of semi open SOM) and semi closed (SCM) M-sets in multiset topological spaces.With this generalization of the notions of open and closed sets in M-topology, we generalize the concept of…

Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…

In this paper, concepts of (topological) FS-approximation spaces are introduced. Representations of FS-domains and BF-domains via (topological) FS-approximation spaces are considered. It is proved that the collection of CF-closed sets in an…

From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of…

We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…

Duistermaat introduced the concept of ``real locus'' of a Hamiltonian manifold. In that and in others' subsequent works, it has been shown that many of the techniques developed in the symplectic category can be used to study real loci, so…

Polynomial splines are ubiquitous in the fields of computer aided geometric design and computational analysis. Splines on T-meshes, especially, have the potential to be incredibly versatile since local mesh adaptivity enables efficient…

The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…

It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.

We explain connections among several, a priori unrelated, areas of mathematics: combinatorics, algebraic statistics, topology and enumerative algebraic geometry. Our focus is on discrete invariants, strongly related to the theory of…

We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…

In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of…