Topology
Reference documents in Topology.
Documents in Topology
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This book introduces Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics with the aim of helping the reader achieve a rapid mastery of the essential topics.
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This is an oustanding book on introductory topology (point set topology). The book is short. However, it is solid and complete and the proofs presented by the author are surprisingly optimised: very concise but always clear.
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This lecture notes lead readers through a number of nontrivial applications of metric space topology to analysis, clearly establishing the relevance of topology to analysis. Covers metric space, point-set topology, and algebraic topology, and includes exercises, selected answers.
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This introductory topology book requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book’s clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles.
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Topology is a branch of pure mathematics that deals with the abstract relationships found in geometry and analysis. Written with the mathematician, this book provides a user-friendly, clear, and concise introduction to this fascinating area of mathematics.
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This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space.
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This book gives a comprehensive introduction to the theory of smooth manifolds, maps, and fundamental associated structures with an emphasis on "bare hands" approaches, combining differential-topological cut-and-paste procedures and applications of transversality.
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Differential geometry is a very active field of research and has many applications to areas such as physics and gravity, for example. The papers in this book cover a number of subjects which will be of interest to workers in these areas.
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The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. Develop many algebraic-topological techniques in the special context of smooth Manifolds such as Poincaré duality, etc.
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Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.
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In mathematics, topology is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
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A graduate-level textbook that presents basic topology from the perspective of category theory.
