En esta tesis, se introduce la teoría de grupos de homotopía sobre espacios topológicos. Se presentan los complejos simpliciales y sus poliedros, las aproximaciones simpliciales de aplicaciones continuas entre poliedros ...

En esta tesis, se introduce la teoría de grupos de homotopía sobre espacios topológicos. Se presentan los complejos simpliciales y sus poliedros, las aproximaciones simpliciales de aplicaciones continuas entre poliedros ...

A unital ℓ-group (G; u) is an abelian group G equipped with a translationinvariant lattice-order and a distinguished element u, called order-unit, whose positive integer multiples eventually dominate each element of G. It ...

We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting ...

We introduce the notion of star cluster of a simplex in a simplicial complex. This concept provides a general tool to study the topology of independence complexes of graphs. We use star clusters to answer a question arisen ...

The classical way to study a finite poset (X, ≤) using topology is by means of the simplicial complex ΔX of its nonempty chains. There is also an alternative approach, regarding X as a finite topological space. In this ...

We introduce the non-pure versions of simplicial balls and spheres with minimum number of vertices. These are a special type of non-homogeneous balls and spheres (NH-balls and NH-spheres) satisfying a minimality condition ...

We prove that a connected simplicial complex is uniquely determined by its complex of discrete Morse functions. This settles a question raised by Chari and Joswig. In the 1-dimensional case, this implies that the complex ...

We prove that for any connected compact CW-complex K there exists aspace X weak homotopy equivalent to K which has the fixed point property, that is,every continuous map X -> X has a fixed point. The result is known to be ...