Topology with Applications
Topology with Applications
A modern introduction to point-set topology with applications drawn from topological data analysis. Topics include open and closed sets, limits, continuity, connectedness, compactness, subspaces, product spaces, and quotient spaces. Additional topics include a study of common spaces found in applications along with implementation of persistent homology and Mapper algorithms. Further topics from algebraic topology, homotopy theory, and classical results from point-set topology to be covered as time permits.