we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

We present new Furi-Pera theorems for acyclic maps between topological spaces. 1. Introduction. In this paper, we present new Furi-Pera theorems [6, 7] for acyclic maps between Hausdorff topological spaces. The main result in our paper is based on a new Leray-Schauder alternative [1] for such maps which in turn is based on the notion of compactly null-homotopic. We first recall some results and...

In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group Iso (U) of isometries of Urysohn’s universal complete separable metric space U, equipped with the compact-open topology, acts upon an arbitrary compact space, it has a fixed point. The ...

We identify four countable topological spaces S2, S1, SD, and S0 which serve as canonical examples of topological spaces which fail to be quasi-Polish. These four spaces respectively correspond to the T2, T1, TD, and T0-separation axioms. S2 is the space of rationals, S1 is the natural numbers with the cofinite topology, SD is an infinite chain without a top element, and S0 is the set of finite...

The paper presents an introduction to computer topology with applications to image processing and computer graphics. Basic topological notions such as connectivity, frontier, manifolds, surfaces, combinatorial homeomorphism etc. are recalled and adapted for locally finite topological spaces. The paper describes data structures for explicitly representing classical topological spaces in computer...

In Lecture 4, we learned about an algebraic method for describing and classifying structures. In this lecture, we look at using algebra to find combinatorial descriptions of topological spaces. We begin by looking at an equivalence relation called homotopy that gives a classification of spaces that is coarser that homeomorphism, but respects the finer classification. That is, two spaces that ha...

In Lecture 4, we learned about an algebraic method for describing and classifying structures. In this lecture, we look at using algebra to find combinatorial descriptions of topological spaces. We begin by looking at an equivalence relation called homotopy that gives a classification of spaces that is coarser that homeomorphism, but respects the finer classification. That is, two spaces that ha...

In this paper,  it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying conver...

In this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.