Topology by Harvard University

Introduction to Topology by Alex Kuronya

This note covers Basic concepts, Constructing topologies, Connectedness, Separation axioms and the Hausdorff property, Compactness and its relatives, Quotient spaces, Homotopy, The fundamental group and some applications, Covering spaces and Classification of covering spaces.

Author(s): Alex Kuronya

102 Pages

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.

Author(s): Professor Denis Auroux

113 Pages

Topology Notes and Problems

This PDF covers the following topics related to Topology : Topology of Metric Spaces, Topological Spaces, Basis for a Topology, Topology Generated by a Basis, Infinitude of Prime Numbers, Product Topology, Subspace Topology, Closed Sets, Hausdorff Spaces, and Closure of a Set, Continuous Functions, A Theorem of Volterra Vito, Homeomorphisms, Product, Box, and Uniform Topologies, Compact Spaces, Quotient Topology, Connected and Path-connected Spaces, Compactness Revisited, Countability Axioms, Separation Axioms, Tychonoff’s Theorem.

Author(s): IIT Kanpur

37 Pages

Topology by Ali Sait Demir

This PDF covers the following topics related to Topology : Preliminaries, Metric Spaces, Topological Spaces, Constructing Topologies, Closed Sets and Limit Points, Continuous Functions, Product and Metric Topologies, Connected Spaces, Compact Spaces, Separation Axioms, Countability Properties, Regular and Normal Spaces.

Author(s): Ali Sait Demir

64 Pages

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.

Author(s): Tom Leinster

85 Pages

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.

Author(s): Ralph L. Cohen and Alexander A. Voronov

95 Pages

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.

Author(s): Prof. James Munkres

NA Pages

Introduction to Topology by David Mond

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

Author(s): David Mond

103 Pages

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.

Author(s): University of California, Riverside

156 Pages

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.

Author(s): John Rognes

100 Pages

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.

Author(s): C. McMullen

90 Pages

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.

Author(s): Renzo Cavalieri

118 Pages