Keywords used: Topology -Dugundji-.pdf, general topology, homotopy theory, Dugundji extension theorem, Munkres vs Dugundji, topology textbook PDF.
The 500+ problems range from routine verification ("Show that T1 is hereditary") to mini-research projects ("Prove the Dugundji Extension Theorem").
Unlike the friendly, conversational tone of Munkres (which is the standard for most undergrads), Dugundji assumes you are an adult. The PDF opens not with hand-holding, but with a brisk introduction to classes and proper classes —a nod to the Kelley/Mac Lane school of thought. If you are expecting colorful diagrams every other page, you will be disappointed. The diagrams here are sparse, functional, and almost primitive in the scanned copy.
His section on contains the famous exercise: "A topological space is T1 iff every singleton is closed." That is the warm-up . The final exercise in that section usually takes an hour.
