Courses

A study of topological spaces. Topics include topologies of real numbers, metric spaces, homeomorphism, compactness and connectedness, product and quotient topological spaces.

An introduction to topology with emphasis on the geometric aspects of the subject. Topics covered include surfaces, topological spaces, open and closed sets, continuity, compactness, connectedness, product spaces, and identification and quotient spaces.

A course in point-set topology emphasizing topological spaces, continuous functions, connectedness, compactness, countability, separability, metrizability, CWcomplexes, simplicial complexes, nerves, and dimension theory.

Definition of topologies; closure; continuity; finite product topology; metric spaces; connectedness; completeness and compactness (in particular, in metric spaces).

An introduction to topology with emphasis on the geometric aspects of the subject. Topics covered include surfaces, topological spaces, open and closed sets, continuity, compactness, connectedness, product spaces, and identification and quotient spaces.

Separation and countability axioms, covering properties, completeness, connectedness, metric spaces and metrizability, product and quotient spaces, function spaces.

Product topology; quotient spaces; countability and separation axioms; Tychonoff's theorem; homotopy; manifolds; partitions of unity.

A continuation of MA 542. Topics covered include the fundamental group, triangulations, classification of surfaces, homology, the Euler-Poincare formula, the Borsuk-Ulam theorem, the Lefschetz fixed-point theorem, knot theory, covering spaces, and applications.

Homotopy, elementary properties of retracts, fundamental groups, covering spaces, computations of fundamental groups.

This course covers the fundamental concepts and tools of algebraic topology. Topics include the fundamental group, covering spaces, homotopy type, the higher homotopy groups, singular homology theory, and the computation of homology groups via exact sequences and applications.