A first-year graduate course in topology. Set theory, topological spaces, connectivity, compactness, separation conditions, and the Tychonoff theorem. The continuation of 523. Topics might include compactifications, metrization theorems, function spaces, completeness, and the fundamental group. The advanced graduate topology course.
Topics vary depending on the instructor.
Math 526, Topology II Same as 525. An introduction to dynamical systems including the study of measure preserving transformations, entropy and information, and the iteration of continuous self maps of compact metric spaces. An introduction to ergodic theory that develops the basic properties of measure-preserving automorphisms of probability spaces. A survey of the basic definitions and major fundamental results in topological groups. An introduction to the axioms of set theory and constructibility.