Introduction to metric & topological spaces:For the second year LMD mathematics students

Abstract

This course aims to provide a comprehensive and accessible introduction to the fundamental concepts of metric spaces, topological spaces, complete spaces, compact spaces, and connected spaces. These mathematical structures form the backbone of modern analysis and topology, and they have wide-ranging applications in fields such as geometry, functional analysis, and theo- retical physics. Understanding these spaces is essential for anyone wishing to pursue advanced studies in mathematics or related disciplines.