Foundations of Topology

Catalog description

Foundations of Topology. Topology - an abstract cousin of geometry -- is the branch of mathematics that deals with connectivity, vicinity, the types of "holes" an object can have, and how these properties interact with continuous functions. Familiarity with the basic intuition and vocabulary of topology is essential for modern working theoretical mathematicians. On one hand, this course will vastly generalize many of the topological ideas encountered in MAT 316, including open/closed/compact sets and the notions of distance, convergence, connectedness, and continuity. On the other hand, it will provide students with important exercise in rigorous proofwriting and abstract reasoning, leading to a much broader overall perspective on the structure of mathematical objects. Prerequisite: MAT-316.