RT info:eu-repo/semantics/masterThesis
T1 Teoría de homotopía digital
A1 Jerez Santana, Karim Omar
K1 Imagen digital - Topología digital - Homotopía digital - Teoría
de homotopía - Espacios de funciones - Espacios de caminos - Cofibración -
Categoría de Lusternik-Schnirelmann - Grupo fundamenta
K1 Digital image - Digital topology - Digital homotopy - Homotopy
theory - Function spaces - Path spaces - Cofibration - Lusternik–Schnirelmann
category - Fundamental group
AB The aim of this master’s thesis is to develop an introduction to homotopy theoryin digital topology, which is a field that studies and analyzes digital images. Theprocedure of the project consists of transferring the usual concepts in algebraictopology to this new context. This topic is not new in the scientific literature,but the distinct attemps to establish a full theory have been unsuccessful,because the achieved results are too rigid, without applicability and do notconnect very well with non-digital context. Therefore, new and significantadvances in this field have been reported. In this sense, the importance of thesubdivision of a digital image has been highlighted, which has made it possibleto deal with new notions such as digital cofibration, for example. Also, newdigital analogs will be established for concepts such as function spaces, pathspaces and the fundamental group. In order to achieve this, we introduce someusual properties into this setting such as the homotopy extension propertyfor cofibrations or the homotopy lifting property. Along the thesis, we alsopresent several interesting examples which illustrate all the theoretical results
YR 2023
FD 2023
LK http://riull.ull.es/xmlui/handle/915/32667
UL http://riull.ull.es/xmlui/handle/915/32667
LA es
NO Máster Univ. en Modelización e Invest.Matemática, Estadística y Computación
DS Repositorio institucional de la Universidad de La Laguna
RD 21-nov-2024