Introduction to Metric Spaces
Metric spaces get built from the ground up in this MIT OpenCourseWare course, starting with the definition of a metric and moving through open and closed sets, continuous functions treated topologically, function spaces, completeness, and compactness. The course materials include lecture notes and problem sets that work through proofs step by step, the kind of groundwork needed before tackling real analysis or general topology. Compactness and completeness get particular attention, since these are the properties that make metric spaces useful for later work in analysis. As with other MIT OpenCourseWare offerings, all materials are free to access online, with no certificate attached. The course assumes some prior exposure to proof-based mathematics but does not require any topology background, making it a reasonable entry point for students moving from calculus into more abstract mathematics.