Ilmi Metric Spaces by Muhammad Amin is an essential textbook designed for B.A and B.Sc Mathematics students. This book provides a clear, systematic, and exam-oriented approach to understanding Metric Spaces, a fundamental concept in Analysis and Topology.

With detailed explanations, solved examples, and step-by-step proofs, this book ensures a strong conceptual foundation in distance functions, continuity, compactness, and convergence. Whether you are preparing for university exams, entry tests, or self-study, this book is a valuable resource for mastering Metric Spaces.

Ilmi Metric Spaces

📖 Key Features:

✅ Complete Coverage of Metric Spaces – Covers core concepts, definitions & theorems
✅ Easy-to-Understand Explanations – Uses simple language & structured learning approach
✅ Solved Examples & Practice Questions – Enhances problem-solving skills
✅ Logical Proofs & Step-by-Step Solutions – Ensures clarity & conceptual understanding
✅ University Exam-Oriented Approach – Includes important theorems & past exam questions
✅ Perfect for B.A & B.Sc Mathematics Students – Designed according to the latest syllabus

📚 Topics Covered:

📌 Introduction to Metric Spaces
📌 Open & Closed Sets in Metric Spaces
📌 Convergence, Continuity & Compactness
📌 Complete Metric Spaces & Banach’s Fixed Point Theorem
📌 Topology of Metric Spaces
📌 Connectedness & Completeness
📌 Applications of Metric Spaces in Analysis & Topology
📌 Solved Problems & Theorem Proofs

Table of Contents 

Preliminaries
Metrics on Sets
Open Balls and Open Sets
Neighbourhoods
Interior
Closed Sets
Closure
Forntier and Exterior
Subspaces
Sequences in metrics spaces