Point-Set Topology: Course
by Peter Saveliev
Publisher: Intelligent Perception 2014
This is an introductory, one semester course on point-set/general topology and its applications. Elementary topology. Topics include topologies, separation axioms, connectedness, compactness, continuity, and metric spaces. It is intended for advanced undergraduate and beginning graduate students.
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by John McCleary - American Mathematical Society
A focused introduction to point-set topology, the fundamental group, and the beginnings of homology theory. The text is intended for advanced undergraduate students. It is suitable for students who have studied real analysis and linear algebra.
by Alex Kuronya
Contents: 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; etc.
by Victor Porton - Mathematics21.org
I introduce the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces. Funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details concept of uniformity.
by Allen Hatcher - Cornell University
These are lecture notes from the first part of an undergraduate course in 2005, covering just the most basic things. From the table of contents: Basic Point-Set Topology; Connectedness; Compactness; Quotient Spaces; Exercises.