Topological spaces, continuity; connectedness, compactness; separation axioms and Tietze extension theorem; function spaces.
Additional Requirements for Graduate Students: Extra homework problems on weekly homework.
Athena Title
Point Set Topology
Prerequisite
(MATH 3100 or MATH 3100H or MATH 3100W) and (MATH 3200 or MATH 3200W or CSCI 2610 or CSCI 2610E or MATH 3510 or MATH 3510H)
Semester Course Offered
Offered every year.
Grading System
A - F (Traditional)
Student learning Outcomes
Students are expected to learn the basic results of point set topology. This will enable students to pursue advanced topics in analysis, geometry, and topology.
Students will learn the definition of topology, the definition of continuity on a topological space, compactness, connectedness, separation axioms, and the Tietze extension theorem for continuous functions. These concepts and results have a wide range of applications in other areas of mathematics and will prepare students for additional advanced work.
Topical Outline
Topological spaces and continuous functions
Closures, interiors, and limit points
Topology of metric spaces
Constructions of topologies, including subspace, quotient, and product topologies
Connectedness and path-connectedness
Compactness and its consequences
Bases for topologies and countability axioms
Hausdorff and other separation axioms
Additional topics determined by the instructor, which may include embedding and metrization theorems, dimension theory, or the fundamental group
