In this work we present the basic properties of the Khalimsky topology on Z 2 . This topology is compared with the Marcus-Wyse ...

The main goal of this proyect is to deepen in the study of the Convergence Spaces which are a generalization of the ...

The notions of filter and ultrafilter are introduced in the field of General Topology to extend the notion of convergence ...

Čech closure spaces were defined by Čech in [3] and are obtained from Kuratowsky closure operator by omitting the idempotent ...

We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, ...

The main goal of this Final Degree Project is the study of pretopological spaces. Being more precise, certain properties ...

The goal of this work is to study the theory of pretopological spaces and some applications. Starting with the key notion ...

The main goal of this work is to introduce the different kinds of combinatorial structures used in topological data analysis. ...

We obtain the number of non-homologically equivalent excellent discrete Morse functions defined on compact orientable surfaces. This work is a continuation of the study which has been done in [2, 4] for graphs.

This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete ...

The aim of this paper is to study the notion of critical element of a proper discrete Morse function defined on non-compact ...

As a sequel of [4] Ayala, R., E. Dom´ıguez, A. R. Franc´es and A. Quintero, Homotopy in Digital Spaces, Discrete and Applied ...

We present an algorithm which defines a discrete Morse function in Forman’s sense on an infinite surface including a study of the minimality of this function.

The main contribution of this paper is a new “extrinsic” digital fundamental group that can be readily generalized to ...

Esta memoria está dedicada a la extensión para complejos simpliciales infinitos de los conceptos y resultados de la teoría ...

In this note we show that 1-skeletons and 2-skeletons of n-pseudomanifolds with full boundary are (n+ 1)-connected graphs and n-connected 2-complexes, respectively. This generalizes previous results due to Barnette and Woon.

This paper is devoted to prove a Digital Index Theorem for digital (n − 1)-manifolds in a digital space (Rn, f), where f ...

This paper contains a study of the connectivity of infinite graphs and 2-complexes. Various connectivity types are defined ...

In R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, J. Rubio. A Polyhedral Approach to Digital Topology a new framework ...

Moore spaces are de ned in proper homotopy theory. Some results on the existence and uniqueness of those spaces are proven. An example of two non properly equivalent Moore spaces is given.

We introduce and study proper homotopy invariants of the Lusternik-Schnirelmann type, p-cat (-), p-Cat(-), and cat e(-) ...

This note gives conditions which assure that the one-point compactification of an open manifold is a manifold. This result is used to show that the homotopical characterization of Rn (n ≥ 4) can be derived from the Poincaré Conjecture.

This work presents a classification of the proper homotopy types of locally finite 1-dimensional CW-complexes.

This paper gives an axiomatical approximation to Bordism Theory. It proves those properties of a geometrical nature that a class of models must satisfy to develop a bordism theory in an abstract category.

The purpose of this note is to prove the exponential law for uniformly continuous proper maps.