Topology: (Book Series P-11/24) (Mastering Mathematical Sciences : Complete 24-Book Series for CSIR NET, JRF, GATE, SET & Ph.D. Entrance Exams)

By Dr Jitendra Singh

This book is thoughtfully designed for aspirants of the CSIR NET (JRF) in Mathematical Sciences , with a focused emphasis on topology , an essential part of the examination syllabus. Featuring over 100 multiple-choice questions (MCQs) per chapter , it aims to provide a complete learning and practice resource that strengthens both conceptual understanding and problem-solving speed. The material is organized into four well-structured chapters, progressively building a solid foundation and preparing students for both theoretical and applied aspects of topology. Chapter 1: Foundations of Topology Introduces the basic ideas of topological spaces, bases, sub-bases, and dense sets. It equips students with fundamental concepts that are crucial for deeper studies in topology and real analysis. Chapter 2: Subspace and Product Topologies Focuses on important constructions in topology. Students learn about subspace topologies inherited from larger spaces, and product topologies formed through Cartesian products--concepts that are vital for understanding advanced structures and spaces. Chapter 3: Separation Axioms Delves into key separation properties like T0T_0T0, T1T_1T1, and T2T_2T2 (Hausdorff spaces), helping students differentiate between various topological spaces. This chapter connects topology with analytical and geometrical reasoning, essential for exam success. Chapter 4: Connectedness and Compactness Covers two major ideas--connected sets and compact sets. Students explore how connectedness defines the structure of a space and how compactness ensures the existence of limit points, making these topics indispensable for advanced mathematical analysis. Throughout the book, each topic is accompanied by: Clear explanations of definitions and theorems. Carefully selected examples to illustrate concepts. A rich collection of MCQs, including conceptual, analytical, and application-based problems. Exercises to build confidence and improve speed and accuracy for the CSIR NET (JRF) exam. This book is intended to serve both as a comprehensive study guide and as a rigorous practice manual . By the end of the book, students will have a strong grasp of topology and will be well-prepared to tackle competitive examinations with clarity, confidence, and precision.

• Format: Hardcover
• Language: English
• ISBN: B0F5P52R75
• ISBN13: 9798280621688
• Release Date: April 2025
• Publisher: Independently published
• Length: 203 Pages
• Dimensions: 9.0" x 0.7" x 6.0"