Year: 2024
Type: article
Abstract: Traditionally, the concept of points and neighborhood structures has been quite dominant in defining and further analyzing various properties in the study of topological spaces. In pointless topology-or point-free topology, also referred to as locale theory-the key emphasis is shifted from points to lattices of open sets. In addition to gaining further insight into spatial properties, this approach has important implications in fields like theoretical computer science, logic, and categorical theory. It is the purpose of the present work to be mainly interested in issues of the foundation of point-free topology: locales, frames, mutual relationships between them; the ways of interpreting classical topological concepts in the new language and the strong and weak points of such a point-free view. In the process, we focus on some of the significant applications of point-free topology, both within mathematics and beyond. The present paper is an attempt to give a broad overview of pointfree topology, discussing both its theoretical basis and its practical significance.
Source: Wasit Journal of Pure sciences
DOI: 10.31185/wjps.528
Author: Nidaa Hasan
Institution: Al-Muthanna University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4402975738