{"product_id":"topology-book-series-p-11-24-9798343137057","title":"Topology: (Book Series P-11\/24)","description":"\u003cp\u003e • Author(s): Preety Verma\u003cbr\u003e • Publisher: Independently Published\u003cbr\u003e • Publisher Imprint: Independently Published\u003cbr\u003e • BISAC: Geometry - Analytic\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book is designed for aspirants of the CSIR NET (JRF) in Mathematical Sciences, with a focused approach on topology-an essential part of the exam syllabus. It aims to provide students with a deep understanding of fundamental topological concepts, structured across four well-organized chapters.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eChapter 1\u003c\/b\u003e begins with the foundations of \u003cb\u003ebasic topology\u003c\/b\u003e, introducing the concept of \u003cb\u003etopological spaces\u003c\/b\u003e and the \u003cb\u003ebasis for a topology\u003c\/b\u003e. The chapter further discusses \u003cb\u003edense sets\u003c\/b\u003e and their significance in analysis, equipping students with core tools essential for deeper mathematical exploration.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eChapter 2\u003c\/b\u003e addresses \u003cb\u003esubspace and product topology\u003c\/b\u003e, starting with the definition and examples of \u003cb\u003esubspace topology\u003c\/b\u003e and moving towards the construction of \u003cb\u003eproduct topology\u003c\/b\u003e through \u003cb\u003eCartesian products\u003c\/b\u003e. This chapter provides clarity on these key constructions, helping students grasp their practical applications in both theoretical and applied contexts.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eChapter 3\u003c\/b\u003e explores the \u003cb\u003eseparation axioms\u003c\/b\u003e-including \u003cb\u003eT₀, T₁, \u003c\/b\u003e and \u003cb\u003eT₂\u003c\/b\u003e-with particular emphasis on \u003cb\u003eHausdorff spaces\u003c\/b\u003e. These axioms are pivotal for distinguishing between different types of topological spaces and are of great importance in both analysis and geometry, making them critical for exam preparation.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eChapter 4\u003c\/b\u003e delves into two of the most significant concepts in topology: \u003cb\u003econnectedness\u003c\/b\u003e and \u003cb\u003ecompactness\u003c\/b\u003e. It provides an in-depth discussion on \u003cb\u003econnected sets\u003c\/b\u003e, which help define the structure of topological spaces, and the concept of \u003cb\u003ecompactness\u003c\/b\u003e, which plays a vital role in analysis, particularly in ensuring the existence of limit points and convergence in various contexts.\u003c\/p\u003e\u003cp\u003eThroughout the book, each concept is accompanied by detailed \u003cb\u003eexamples\u003c\/b\u003e and \u003cb\u003eexercises\u003c\/b\u003e, allowing students to apply the theory and strengthen their problem-solving skills. The goal is to provide a clear, systematic guide that will enable students to build a solid foundation in topology and approach the CSIR NET (JRF) exam with confidence.\u003c\/p\u003e","brand":"Independently Published","offers":[{"title":"Paperback","offer_id":45559516987543,"sku":"9798343137057","price":942.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9798343137057.webp?v=1768595508","url":"https:\/\/atlanticbooks.com\/products\/topology-book-series-p-11-24-9798343137057","provider":"Atlantic Books","version":"1.0","type":"link"}