Learning

Topological Spaces: Continuity, Compactness, and Connectedness

Set Theory and Functions → Quotient Spaces

A rigorous graduate-level path through the foundations of point-set topology, from set-theoretic and real-analysis prerequisites to the core concepts of topological spaces, continuity, separation, compactness, connectedness, and the constructions of product and quotient spaces. Emphasis is on proof and conceptual understanding.