Fundamentals of Point-Set Topology

About this course:

Point-set topology is the branch of mathematics that deals with collections of points endowed with sufficient structure to make meaningful the notions of closeness, separation, and convergence. Beginning with familiar notions concerning open sets, closed sets, and convergence on the real number line and Euclidean plane, this course systematically develops the theory of arbitrary topological spaces. Topics include bases and subbases, separation axioms (Hausdorff, regular, and normal spaces), countability (first- and second-countable spaces), compactness and compactification, connectedness, and convergence (nets and filters). Instruction emphasizes examples and problem solving. The course appeals to those seeking a better understanding of the algebraic and geometric underpinnings of common mathematical constructs.