Point Set Topology

Notes on Basic 3 Manifold Topology

This note contains below topics, is a prere quisite for almost everything else, while some of the later parts o, are u sed in, Canonical Decomposition, Prime Decomposition, Torus Decomposition, Seifert Manifolds, Torus Bundles and SemiBundles, Homotopy Properties, Canonical Decomposition The rst section of this.

Author(s): Allen Hatcher

75 Pages

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

Lecture notes on generalized Heegaard splittings

This note contains below topics, Heegaard splittings, Generalized Heegaard splittings, Show Remark, Hence we have Claim, We give a proof of Proposition, By Lemma, Show the claim in the proof of Theorem, We prove Theorem, It follows from Lemma.

Author(s): Toshio Saito, Martin Scharlemann, Jennifer Schultens

66 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 I and II by Chris Wendl

This note describes the following topics, Metric spaces, Topological spaces, Products, sequential continuity and nets, Compactness, Tychonoffs theorem and the separation axioms, Connectedness and local compactness, Paths, homotopy and the fundamental group, Retractions and homotopy equivalence, Van Kampens theorem, Normal subgroups, generators and relations, The Seifertvan 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 EilenbergSteenrod axioms, The MayerVietoris sequence, Mapping tori and the degree of maps, ocal mapping degree on manifolds Degrees, triangulations and coefficients, CWcomplexes, Invariance of cellular homology.

Author(s): Chris Wendl

382 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