MATH313

The notion of "closeness" underlies many important mathematical concepts, such as limits and continuity. Topology is the careful study of what this notion means in abstract spaces, leading to a thorough understanding of continuous mappings and the properties of spaces that they preserve. Topics may include metric spaces, topological spaces, continuity, compactness, connectedness, homotopy theory, fixed-point theorems, and applications of these topics in areas such as geographic information systems, robotics, and game theory. Prerequisite(s): MATH 205, 206, and 221.