Chapter 8

प्रस्तावना (Preface)

The Preface introduces the textbook 'वास्तविक विश्लेषण एवं दूरीक समष्टि' (Real Analysis & Metric Space), published by Vardhman Mahaveer Open University, Kota. This book is designed according to the curriculum for B.Sc. Part II Mathematics, Paper I. The Preface emphasizes the effort to make the language simple, engaging, and easy to understand. It acknowledges the mathematical nature of the subject and incorporates English terminology alongside Hindi for clarity. The book is written by expert authors and references standard texts to ensure factual accuracy. The Preface also expresses gratitude to the creators of these reference works. The book aims to guide students preparing for competitive exams and provide a comprehensive resource for learning real analysis and metric spaces.

• Book is structured for B.Sc. Part II Mathematics, Paper I.
• Language is simple, engaging, and uses both Hindi and English terminology.
• Written by expert authors referencing standard texts.
• Useful for competitive exam preparation.
• Acknowledges contributors and expresses gratitude.
• 📌 वास्तविक विश्लेषण (Real Analysis): Study of real numbers and their properties.
• 📌 दूरीक समष्टि (Metric Space): Mathematical structure involving distance concepts.

इकाई संख्या (Unit Number)

This section provides an overview of the units (chapters) covered in the textbook. Each unit covers a specific topic in real analysis and metric spaces. The units are numbered and titled in both Hindi and English, with corresponding page numbers. The list includes foundational topics such as the real number system, topological properties, sequences, continuity, derivatives, Riemann integration, uniform convergence, metric spaces, open and closed sets, subspaces, product spaces, compactness, and connectedness. This structure ensures a logical progression from basic to advanced concepts.

• Units cover all major topics in real analysis and metric spaces.
• Each unit is titled in Hindi and English.
• Page numbers are provided for easy reference.
• Topics progress from real numbers to advanced metric space concepts.
• 📌 इकाई (Unit): Chapter or section of the textbook.
• 📌 वास्तविक संख्या निकाय (Real Number System): Foundation of real analysis.
• 📌 सांतत्य (Continuity): Property of functions.