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The text emphasizes rigorous conceptual understanding rather than only “big theorems,” using a unified selection of topics. It highlights the relationships among metric geometry, point-set topology, differential topology, and differential geometry, and supports flexible course use with optional sections.","Introduction to Topology and Geometry  \n[OceanofPDF.com](OceanofPDF.com)  \nIntroduction to Topology and Geometry  \nCiprian Manol escu  \nPRINCETON UNIVERSITY PRESS  \nPRINCETON & OXFORD  \n[OceanofPDF.com](OceanofPDF.com)  \nCopyright © 2026 by Ciprian Manolescu  \nPrinceton University Press is committed to the protection of copyright and the intellectual property our authors entrust to us. Copyright promotes the progress and integrity of knowledge created by humans. By engaging with an authorized copy of this work, you are supporting creators and the global exchange of ideas. As this work is protected by copyright, any reproduction or distribution of it in any form for any purpose requires permission; permission requests should be sent to [permissions@press.princeton.edu](permissions@press.princeton.edu. Ingestion or use)[. Ingestion or use](permissions@press.princeton.edu. Ingestion or use) of any Princeton University Press intellectual property for any AI purposes is strictly prohibited without a license to do so; licensing requests should be sent [to ](to DigitalLicensing@press.princeton.edu)[DigitalLicensing@press.princeton.edu](to DigitalLicensing@press.princeton.edu).  \nPublished by Princeton University Press  \n41 William Street, Princeton, New Jersey 08540  \n99 Banbury Road, Oxford OX2 6JX  \n[press.princeton.edu](press.princeton.edu)  \nGPSR Authorized Representative: Easy Access System Europe-Mustamäe tee 50, 10621 Tallinn, Estonia, [gpsr.requests@easproject.com](gpsr.requests@easproject.com)  \nAll Rights Reserved  \nISBN 9780691284477  \nISBN (pbk.) 9780691284620 ISBN (epub) 9780691291727 ISBN (PDF) 9780691284613  \nVersion 1.0  \nLibrary of Congress Control Number: 2026938977 British Library Cataloging-in-Publication Data is available Editorial: Diana Gillooly and Abigail Corcelli  \nProduction Editorial: Nathan Carr  \nText Design: Wanda España  \nJacket/Cover Design: Wanda España  \nProduction: Lauren Reese  \nCopyeditor: Jennifer McClain  \nJacket image credit: Kseniya-Omega / Alamy  \nAll math content has been captured both as MathML to best enable assistive technologies (such as screen readers) and as images to enable display on reading systems which do not support MathML. If the MathML content does not display on your e-reader, please contact the vendor through which you purchased your ebook.  \n[OceanofPDF.com](OceanofPDF.com)  \nContents  \nPreface vii  \n1  Introduction 1  \n1.1  Overview 1  \n1.2  Prerequisites 3  \n2  Metric Geometry 14  \n2.1  Metric Spaces 14  \n2.2  Continuity 19  \n2.3  Isometries and Homeomorphisms 21  \n2.4  Compactness 25  \n2.5  Completeness 29  \n2.6  Topological Properties of Metric Spaces 32  \n3  Point-Set Topology 34  \n3.1  Topological Spaces 34  \n3.2  Examples 36  \n3.3  Bases 40  \n3.4  Interior and Closure 44  \n3.5  Countability Axioms 47  \n3.6  Separation Axioms 51  \n3.7  Compactness 57  \n3.8  Order Topologies 61  \n3.9  Connectedness 65  \n3.10 Product Topologies 71  \n3.11 Quotient Topologies 77  \n3.12 Topological Manifolds 83  \n3.13 Embeddings 93  \n3.14 Triangulations 98  \n4  Differential Topology 105  \n4.1  The Inverse Function Theorem 105  \n4.2  The Implicit Function Theorem 112  \n4.3  Smooth Manifolds 116  \n4.4  Examples 123  \n4.5  Derivatives 127  \n4.6  More on the Tangent Space 131  \n4.7  Immersions and Embeddings 140  \n4.8  Submanifolds 146  \n4.9  Submersions 152  \n4.10 Transversality 159  \n4.11 Sard’s Theorem 167  \n4.12 The Tangent Bundle 180  \n4.13 Embedding Theorems 184  \n4.14 Morse Functions 192  \n5  Differential Geometry 200  \n5.1  Riemannian Manifolds 200  \n5.2  The Distance Function 206  \n5.3  Riemannian Isometries 210  \n5.4  Non-Euclidean Geometries 213  \n5.5  Curves 219  \n5.6  Surfaces 225  \n5.7  Gauss’s Theorema Egregium 232  \nBibliography 239  \nIndex 241  \n[OceanofPDF.com](OceanofPDF.com)  \nPreface  \nThis textbook is tailored to advanced undergraduates and beginning graduate students. Its aim is to familiarize the readers with a few of the most important concepts in geometry and topology","cbCaisqljuV8fzSk","https://ap.wps.com/l/cbCaisqljuV8fzSk","pdf",9957749,4,1,360,"English","en",105,"# Preface\n# 1 Introduction\n## 1.1 Overview\n## 1.2 Prerequisites\n# 2 Metric Geometry\n## 2.1 Metric Spaces\n## 2.2 Continuity\n## 2.3 Isometries and Homeomorphisms\n## 2.4 Compactness\n## 2.5 Completeness\n## 2.6 Topological Properties of Metric Spaces\n# 3 Point-Set Topology\n## 3.1 Topological Spaces\n## 3.2 Examples\n## 3.3 Bases\n## 3.4 Interior and Closure\n## 3.5 Countability Axioms\n## 3.6 Separation Axioms\n## 3.7 Compactness\n## 3.8 Order Topologies\n## 3.9 Connectedness\n## 3.10 Product Topologies\n## 3.11 Quotient Topologies\n## 3.12 Topological Manifolds\n## 3.13 Embeddings\n## 3.14 Triangulations\n# 4 Differential Topology\n## 4.1 The Inverse Function Theorem\n## 4.2 The Implicit Function Theorem\n## 4.3 Smooth Manifolds\n## 4.4 Examples\n## 4.5 Derivatives\n## 4.6 More on the Tangent Space\n## 4.7 Immersions and Embeddings\n## 4.8 Submanifolds\n## 4.9 Submersions\n## 4.10 Transversality\n## 4.11 Sard’s Theorem\n## 4.12 The Tangent Bundle\n## 4.13 Embedding Theorems\n## 4.14 Morse Functions\n# 5 Differential Geometry\n## 5.1 Riemannian Manifolds\n## 5.2 The Distance Function\n## 5.3 Riemannian Isometries\n## 5.4 Non-Euclidean Geometries\n## 5.5 Curves\n## 5.6 Surfaces\n## 5.7 Gauss’s Theorema Egregium\n# Bibliography\n# Index","[{\"question\":\"Who is the textbook intended for?\",\"answer\":\"The book is tailored to advanced undergraduates and beginning graduate students.\"},{\"question\":\"What topics does the book focus on?\",\"answer\":\"It covers metric spaces, topological spaces, and three kinds of manifolds: topological, smooth, and Riemannian.\"},{\"question\":\"How does the book approach learning—proofs or concepts?\",\"answer\":\"The emphasis is on understanding key concepts rigorously, rather than proving only major theorems.\"}]","Introduction to Topology and Geometry - 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