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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.
Author(s): Dr Sheng-Chi Liu
89 Pages 
Lecture notes on Topology by Huynh Quang Vu
This note covers general topology, Geometric topology and differential topology.
Author(s): Huynh Quang Vu
118 Pages
General Topology lecture notes
This note covers introduction, Set theory, Topological spaces, Metric topologies, Connected spaces, Compactness, Advanced material.
Author(s): Thomas Baird
59 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
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