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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
113Pages
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
37Pages
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
64Pages
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.
Author(s): Chris Wendl
382Pages
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
85Pages
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
95Pages
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.
Author(s): Michael Muger
407Pages
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
NAPages
This note explains the following topics: Topology versus Metric Spaces, The fundamental group, Covering Spaces, Surfaces.
Author(s): David Mond
103Pages
This note covers the following topics: Topological Spaces, Product and Quotient Spaces, Connected Topological Spaces, Compact Topological Spaces, Countability and Separation Axioms.
Author(s): P. Veeramani
143Pages
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
156Pages
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
100Pages
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.
Author(s): Soren Fuglede Jorgensen
93Pages
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
90Pages
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
118Pages
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.
Author(s): Alex Kuronya
102Pages
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.
Author(s): T. W. Korner
102Pages
