General Topology and Analysis

General Topology and Analysis provide a theoretical foundation that supports research in various practical applications. However, students often consider these subjects challenging. In response, the book provides a straightforward and comprehensive presentation of the material. This book covers all the essential topological structures in an abstract manner to understand concepts such as continuity, homeomorphism, and limits. It also delves into metric spaces and complete spaces, which are crucial special cases of topological spaces. Additionally, it explores the fixed-point theorem and its applications and fundamental theorems. It also includes compact topological spaces and connected topological spaces, and it addresses normed vector spaces and continuous linear (or multilinear) applications, which are fundamental tools in functional analysis. Also, the book contains examples that could be useful for students interested in electrical engineering. Moreover, diagrams in the book are designed not only to clarify the specific topic but also to connect that topic with other branches of topology and geometry. The counter-examples, problems, and exercises are well chosen in order of difficulty. This book serves as a textbook for graduate and advanced students interested in math applications to functional analysis, differential equations, computer science, control theory, and optimization.

Yamina Miloudi received her Ph.D. from the University of Oran in Algeria. She is a Full Professor at the University Oran 1 and team leader in the Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO). Her main area of research is Control, EDP and Optimization. She is the author of two mathematics books published by national publishing houses, as well as author and co-author of international publications.