/   Mathematics Books /  

Topology Books

Topology Books

This section contains free e-books and guides on Topology, some of the resources in this section can be viewed online and some of them can be downloaded.

Lecture Notes in General Topology

This note explains the following topics: Continuity, Infinite product spaces, Connectedness and compactness, Tychonoff’s theorem, Compactnesses, Countability and separation axioms, Urysohn’s lemma, Urysohn’s metrisation theorem, Baire category theorem, Quotient spaces and topological groups, Homotopy theory, Covering spaces, Brouwer fixed-point theorem.


s 89Pages

Introduction to Topology by Professor Denis Auroux

This note covers the following topics: Topological Spaces, Bases, Subspaces, Products, Continuity, Continuity, Homeomorphisms, Limit Points, Sequences, Limits, Products, Connectedness, Path Connectedness, Compactness, Uncountability, Metric Spaces,Countability, Separability, and Normal Spaces.


s 113Pages

Topology I and II by Chris Wendl

This note describes the following topics: Metric spaces, Topological spaces, Products, sequential continuity and nets, Compactness, Tychonoff’s theorem and the separation axioms, Connectedness and local compactness, Paths, homotopy and the fundamental group, Retractions and homotopy equivalence, Van Kampen’s theorem, Normal subgroups, generators and relations, The Seifert-van Kampen theorem and of surfaces, Torus knots, The lifting theorem, The universal cover and group actions, Manifolds, Surfaces and triangulations, Orientations and higher homotopy groups, Bordism groups and simplicial homology, Singular homology, Relative homology and long exact sequences, Homotopy invariance and excision, The homology of the spheres, Excision, The Eilenberg-Steenrod axioms, The Mayer-Vietoris sequence, Mapping tori and the degree of maps, ocal mapping degree on manifolds Degrees, triangulations and coefficients, CW-complexes, Invariance of cellular homology.


s 382Pages

General Topology by Tom Leinster

This note covers the following topics: Topological spaces, metric spaces, Topological properties, Subspaces, Compactness, Compact metric spaces, Connectedness, Connected subsets of the real line.


s 85Pages

Notes on String Topology

String topology is the study of algebraic and differential topological properties of spaces of paths and loops in manifolds. Topics covered includes: Intersection theory in loop spaces, The cacti operad, String topology as field theory, A Morse theoretic viewpoint, Brane topology.


s 95Pages

Topology for the working mathematician

This note covers the following topics: Basic notions of point-set topology, Metric spaces: Completeness and its applications, Convergence and continuity, New spaces from old, Stronger separation axioms and their uses, Connectedness. Steps towards algebraic topology, Paths in topological and metric spaces, Homotopy.


s 407Pages

Introduction to Topology Lecture Notes

This note introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems and the fundamental group.


s NAPages

Introduction to Topology by David Mond

This note explains the following topics: Topology versus Metric Spaces, The fundamental group, Covering Spaces, Surfaces.


s 103Pages

General Topology by Shivaji University

This note covers the following topics: Topological spaces, Bases and subspaces, Special subsets, Different ways of defining topologies, Continuous functions, Compact spaces, First axiom space, Second axiom space, Lindelof spaces, Separable spaces, T0 spaces, T1 spaces, T2 – spaces, Regular spaces and T3 – spaces, Normal spaces and T4 spaces, Completely Normal and T5 spaces, Product spaces and Quotient spaces.


s 260Pages

Topology by P. Veeramani

This note covers the following topics: Topological Spaces, Product and Quotient Spaces, Connected Topological Spaces, Compact Topological Spaces, Countability and Separation Axioms.


s 143Pages

Introduction to Topology University of California

This note covers the following topics: Basic set theory, Products, relations and functions, Cardinal numbers, The real number system, Metric and topological spaces, Spaces with special properties, Function spaces, Constructions on spaces, Spaces with additional properties, Topological groups, Stereographic projection and inverse geometry.


s 156Pages

Lecture Notes on Topology by John Rognes

This note describes the following topics: Set Theory and Logic, Topological Spaces and Continuous Functions, Connectedness and Compactness, Countability and Separation Axioms, The Tychonoff Theorem, Complete Metric Spaces and Function Spaces, The Fundamental Group.


s 100Pages

Basic topology

This note will mainly be concered with the study of topological spaces. Topics covered includes: Set theory and logic, Topological spaces, Homeomorphisms and distinguishability, Connectedness, Compactness and sequential compactness, Separation and countability axioms.


s 93Pages

Topology by Harvard University

This note covers the following topics : Background in set theory, Topology, Connected spaces, Compact spaces, Metric spaces, Normal spaces, Algebraic topology and homotopy theory, Categories and paths, Path lifting and covering spaces, Global topology: applications, Quotients, gluing and simplicial complexes, Galois theory of covering spaces, Free groups and graphs,Group presentations, amalgamation and gluing.


s 90Pages

Introduction to Topology by Renzo Cavalieri

This is a collection of topology notes compiled by Math topology students at the University of Michigan in the Winter 2007 semester. Introductory topics of point-set and algebraic topology are covered in a series of five chapters. Major topics covered includes: Making New Spaces From Old, First Topological Invariants, Surfaces, Homotopy and the Fundamental Group.


s 118Pages

Introduction To Topology

This book explains the following topics: Basic concepts, Constructing topologies, Connectedness, Separation axioms and the Hausdorff property, Compactness and its relatives, Quotient spaces, Homotopy, The fundamental group and some application, Covering spaces and Classification of covering space.


s 102Pages

Metric and Topological Spaces

First part of this course note presents a rapid overview of metric spaces to set the scene for the main topic of topological spaces.Further it covers metric spaces, Continuity and open sets for metric spaces, Closed sets for metric spaces, Topological spaces, Interior and closure, More on topological structures, Hausdorff spaces and Compactness.


s 102Pages