Chapter 6

इकाई संख्या

This section presents the unit structure of the textbook 'वास्तविक विश्लेषण एवं दूरीक समष्टि' (Real Analysis & Metric Space). It lists the units and their corresponding page numbers, providing an overview of the topics covered in the course. The units include foundational concepts such as the Real Number System, Topological Properties of Real Numbers, Real Sequences, Continuity, Derivatives, Limits and Continuity for Functions of Two Variables, Riemann Integration, Uniform Convergence of Sequences of Functions, Metric Spaces, Open and Closed Sets, Subspaces and Product Spaces, Compact and Connected Spaces. Each unit is designed to build upon the previous, gradually introducing advanced concepts in real analysis and metric spaces.

• The textbook is divided into 15 units covering real analysis and metric spaces.
• Each unit focuses on a specific topic, such as real numbers, sequences, continuity, derivatives, integration, and metric spaces.
• Page numbers for each unit are provided for easy reference.
• The structure allows for systematic study and progression from basic to advanced topics.
• 📌 Real Number System: The set of numbers including rational and irrational numbers, forming the basis of real analysis.
• 📌 Metric Space: A set with a distance function satisfying certain properties, used to study topology and analysis.

प्रस्तावना

The preface introduces the textbook 'वास्तविक विश्लेषण एवं दूरीक समष्टि', created for the B.Sc. Part II Mathematics course at Vardhman Mahaveer Open University, Kota. The text emphasizes the use of simple, engaging, and accessible language, with appropriate use of English terminology alongside Hindi. The authors have relied on standard references to ensure factual accuracy and clarity. The book is structured to aid both regular study and competitive exam preparation, making it a valuable resource for students.

• The textbook is designed for B.Sc. Part II Mathematics students.
• Language is simple and engaging, with English terms used where necessary.
• Authors have referred to standard texts to ensure accuracy.
• The book is useful for both academic study and competitive exams.
• 📌 Preface: An introductory statement explaining the purpose, scope, and approach of the textbook.