Chapter 3

इकाई संख्या

This section provides the unit-wise structure of the textbook 'वास्तविक विश्लेषण एवं दूरीक समष्टि' (Real Analysis and Metric Spaces) as prescribed by Vardhman Mahaveer Open University, Kota. The table lists the unit numbers, their titles in both Hindi and English, and the corresponding page numbers. This helps students understand the overall layout and progression of the course. The units cover foundational topics in real analysis, including the real number system, topological properties, sequences, continuity, derivatives, functions of two variables, Riemann integration, uniform convergence, metric spaces, open and closed sets, subspaces, product spaces, continuous mappings, compactness, and connectedness.

• The textbook is divided into 15 units, each focusing on a specific topic in real analysis and metric spaces.
• Unit titles are provided in both Hindi and English for clarity.
• Page numbers for each unit are listed, aiding in navigation.
• The structure ensures a logical progression from basic to advanced topics.
• 📌 Real Number System: The set of real numbers and its properties.
• 📌 Topological Properties: Characteristics of real numbers related to topology.
• 📌 Real Sequence: An ordered list of real numbers.

प्रस्तावना

The preface introduces the textbook 'वास्तविक विश्लेषण एवं दूरीक समष्टि' (Real Analysis and Metric Spaces), explaining its purpose and approach. The book is designed for B.Sc. Part II Mathematics students as per the curriculum of Vardhman Mahaveer Open University. The language is intentionally kept simple, engaging, and accessible. English terminology is used alongside Hindi to facilitate comprehension, especially for mathematical terms. The content is authored by subject experts and references standard mathematical texts to ensure accuracy and depth. The preface also expresses gratitude to the authors of these standard references. The book is also intended to aid students preparing for competitive examinations.

• The book is tailored for B.Sc. Part II Mathematics students.
• Simple and engaging language is used for better understanding.
• English mathematical terms are included alongside Hindi.
• Content is written by experienced subject experts.
• References to standard texts ensure reliability.
• The book is also useful for competitive exam preparation.
• 📌 Axiomatic Method: A method of study based on a set of axioms or fundamental principles.
• 📌 Algebraic Structure: A set with one or more operations defined on it.