Introductory Topology: Exercises And Solutions by Mohammed Hichem Mortad – A Practical Problem-Solving Book for Undergra

Introduction

Topology is often called 'rubber-sheet geometry' because it studies properties that remain unchanged under continuous deformations—stretching, twisting, and bending, but not tearing or gluing. For undergraduate students in mathematics and physics, mastering topology requires not just understanding concepts but also solving a wide variety of problems. Introductory Topology: Exercises And Solutions by Mohammed Hichem Mortad, published by World Scientific Publishing Company, is a comprehensive resource designed to build solid problem-solving skills through carefully curated exercises with detailed solutions. This hardcover edition is an essential companion for Indian students preparing for competitive exams or university courses in pure and applied mathematics.

Book Overview

This second edition of the well-received textbook offers a thorough introduction to topology through solved exercises. It is primarily intended for undergraduate students, but it also serves as a valuable reference for teachers and self-learners. The book is structured to guide readers from fundamental concepts to more advanced topics, with each exercise accompanied by a step-by-step solution. The new edition has been significantly expanded: the old 'What You Need To Know' section has been renamed 'Essential Background' and now includes more remarks, proofs, and results for readers' convenience. Additional exercises have also been added, making this edition even more comprehensive than its predecessor.

Key Highlights

• Over 400 solved exercises covering all major topics in introductory topology
• Detailed step-by-step solutions that explain reasoning, not just final answers
• Expanded 'Essential Background' section with proofs of many key results
• New exercises added in the second edition for deeper practice
• Self-contained format suitable for both classroom use and independent study
• Hardcover binding for durability—ideal for Indian libraries and personal collections

Inside the Book

The book begins with a refresher on set theory, metric spaces, and basic topological concepts. Each chapter presents a series of problems that progress from simple to challenging. Solutions are written in clear, mathematical English, often with diagrams described in text. The 'Essential Background' section at the start of each chapter provides the necessary definitions, theorems, and examples, so students can immediately attempt the exercises without flipping to other references. The second edition also includes additional proofs as exercises, encouraging active learning rather than passive reading.

Key Topics

• Topological spaces, bases, and subspaces
• Continuous functions, homeomorphisms, and product spaces
• Connectedness and compactness
• Separation axioms (T0, T1, T2, regular, normal)
• Metric spaces and metrization
• Nets, filters, and convergence
• Quotient spaces and identification maps
• Complete metric spaces and Baire category theorem

Reader Benefits

• Builds problem-solving confidence through guided practice
• Clarifies abstract concepts with concrete, worked-out examples
• Saves time by providing complete solutions—no need to search for hints
• Prepares for exams like JAM, GATE, and university semester tests
• Ideal for self-study with its self-contained structure
• Teachers can use it as a source for assignments and exam questions

Learning Outcomes

By working through this book, students will be able to: define and identify topological spaces and their properties; prove continuity and homeomorphism using open sets; analyze connectedness and compactness in various spaces; apply separation axioms to classify topological spaces; construct product and quotient spaces; understand the role of completeness in metric spaces; and develop rigorous proof-writing skills essential for advanced mathematics.

Who Should Read

This book is ideal for undergraduate students of mathematics and physics in Indian universities who are taking a first course in topology. It is also highly recommended for students preparing for entrance exams such as the Joint Admission Test for MSc (JAM), the Graduate Aptitude Test in Engineering (GATE) in mathematics, and the CSIR-UGC NET. Teachers and lecturers will find it a valuable resource for creating problem sets and tutorial material. Self-learners with a background in real analysis and set theory will also benefit greatly.

About the Author

Mohammed Hichem Mortad is a professor of mathematics at the University of Oran 1 Ahmed Ben Bella, Algeria. He has extensive experience teaching topology and analysis at the undergraduate and graduate levels. His research interests include operator theory, functional analysis, and mathematical physics. Dr. Mortad has authored several textbooks and research papers, and his writing style is known for being clear, rigorous, and student-friendly.

About the Publisher

World Scientific Publishing Company is a leading international academic publisher based in Singapore, with a strong reputation for producing high-quality textbooks and research monographs in mathematics, physics, and engineering. Their titles are widely used in Indian universities and research institutions. This hardcover edition ensures long-lasting use, making it a worthy investment for serious students.

Conclusion

Introductory Topology: Exercises And Solutions is more than just a problem book—it is a complete learning system that combines theory, practice, and solution strategies. Whether you are struggling with the basics or aiming to master advanced concepts, this book provides the structured practice you need. With its expanded content and detailed solutions, it is a must-have for every mathematics student's library. Order your copy from Bookshops.in today and take a confident step toward mastering topology.