Topology for the working mathematician

Point Set Topology

This is a review of the fundamental concepts of general topology. This note contains below topics, Topological Spaces, Continuous Maps, Connectedness, Separation Axioms, Compactness, A Taste of Topology in Functional Analysis.

Author(s): Farzad Shahi

288 Pages

Fans and their applications in General Topology Functional Analysis and Topological Algebra

This note contains below topics, Introduction and survey of main results, Some notation and general tools, Applications of strict Cldfans in General Topology, SFans Ssemifans and Dcofans in topological spaces, Strong Finfans in functions spaces, Strong Finfans in locally convex and Banach spaces with the weak topology, Topological functors and their properties, Constructing Finfans in topological algebras, Constructing fans in free universal algebras, Free objects in some varieties of topologized algebras.

Author(s): Taras Banakh

117 Pages

General Topology by Paul Souverains

This note covers topological spaces, Continuous functions, Compact topological spaces, Compact metric spaces, Separability axioms and theorems, Metrizations.

Author(s): Paul Souverains

323 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 Pathconnected Spaces, Compactness Revisited, Countability Axioms, Separation Axioms, Tychonoffs Theorem.

Author(s): IIT Kanpur

37 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

Topology for the working mathematician

This note covers the following topics, Basic notions of pointset 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.

Author(s): Michael Muger

407 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