{"product_id":"b0gkx32n4b","title":"TOPOLOGY VOLUME 01: Foundations of Metric and Topological Spaces (Bachelor's Degree in Mathematics)","description":"\u003cp\u003eAre you looking for a topology textbook that explains  why  the theory works, not just  how  to apply definitions?\u003c\/p\u003e\n\n\u003cp\u003eTopology Vol. 01 — Foundations of Metric and Topological Spaces  provides a rigorous and carefully motivated introduction to the core concepts of modern topology. Starting from metric spaces and distance functions, this volume guides the reader step by step toward the abstract framework of general topology based on open and closed sets.\u003c\/p\u003e\n\n\u003cp\u003eRather than presenting topology as a collection of isolated definitions, this book emphasizes structure, intuition, and logical development. Historical motivation, precise proofs, and well-chosen examples from functional analysis, differential geometry, and mathematical physics are integrated throughout, ensuring both depth and applicability.\u003c\/p\u003e\n\n\u003cp\u003eWhat you will learn in this volume Metric and Normed Spaces\u003cbr\u003e\nA systematic axiomatic treatment of metrics, including symmetry, identity, and the triangle inequality. Classical examples such as Euclidean spaces, LpL^pLp norms, and the supremum norm are explored, together with applications to spaces of functions. Topics include convergence of sequences, completeness, and homeomorphisms between normed spaces.\u003c\/p\u003e\n\n\u003cp\u003ePseudometric Spaces\u003cbr\u003e\nA fundamental generalization allowing distinct points to have zero distance, essential for quotient constructions and equivalence classes. The induced topology is studied with applications to measurable function spaces (LpL^pLp), fractal structures, and singular measures.\u003c\/p\u003e\n\n\u003cp\u003eContinuous Functions\u003cbr\u003e\nContinuity is presented from two complementary perspectives: the classical ε\\varepsilonε–δ\\deltaδ definition and the topological approach via preimages of open sets. Uniform continuity on compact spaces is analyzed in detail, highlighting its role in global stability.\u003c\/p\u003e\n\n\u003cp\u003eOpen and Closed Sets\u003cbr\u003e\nThe axioms governing unions and intersections, along with the construction of bases and subbases, are developed as the foundation of topological reasoning. This chapter establishes the language used throughout all later areas of topology.\u003c\/p\u003e\n\n\u003cp\u003eConnected Sets\u003cbr\u003e\nThe concept of connectedness as non-separability into disjoint open sets is introduced and analyzed through classical and advanced examples, paving the way for applications in homotopy theory and algebraic topology.\u003c\/p\u003e\n\n\u003cp\u003eSolved and Proposed Exercises\u003cbr\u003e\nOver 200 carefully structured problems, including fully worked solutions, guided strategies, and advanced challenges that connect topology with physics, engineering, and data modeling.\u003c\/p\u003e\n\n\u003cp\u003eWhy this book stands out Rigorous mathematical proofs with clear logical structure\u003c\/p\u003e\n\n\u003cp\u003eStrong pedagogical focus with examples and counterexamples\u003c\/p\u003e\n\n\u003cp\u003eClean layout and reader-friendly typography\u003c\/p\u003e\n\n\u003cp\u003eA solid foundation for advanced topics developed in Volume II\u003c\/p\u003e\n\n\u003cp\u003eIdeal for Undergraduate and graduate students in Mathematics, Physics, Engineering, and Applied Sciences; instructors of Analysis and Topology; researchers and professionals who use topological methods in theory or applications.\u003c\/p\u003e\n\n\u003cp\u003eSeries:  Bachelor’s Degree in Mathematics\u003cbr\u003e\nAuthor:  Helbert Justo Luque Zevallos\u003cbr\u003e\nOrigin:  Arequipa, Peru\u003c\/p\u003e\n\n\u003cp\u003eStrengthen your understanding of the foundations of topology and build the conceptual tools required for advanced mathematical study.\u003c\/p\u003e","brand":"ANT","offers":[{"title":"Ebook","offer_id":52821264859352,"sku":"YSL39242","price":4.5,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0835\/3356\/2072\/files\/81Se-K_iGLL._SY1500.jpg?v=1793103797","url":"https:\/\/www.bookmebay.com\/products\/b0gkx32n4b","provider":"BookMebay","version":"1.0","type":"link"}