An Introduction To General Topology Paul E Long Pdf Link Here

Metric spaces are introduced in Chapter 2 as primary examples, but Chapter 8 focuses on completeness and metric-specific properties.

The heart of the introduction. Long defines a topology, open sets, closed sets, and the axioms (the empty set and whole space are open; finite intersections and arbitrary unions of open sets are open). He provides numerous examples: the discrete topology, indiscrete topology, finite complement topology, and the usual topology on the real line. an introduction to general topology paul e long pdf link

If you absolutely cannot afford it, speak to your mathematics department or library. Many professors keep a desk copy they can share, or they may place the book on course reserve. Remember: topology is about building connections—between spaces, between ideas, and between learners. Respect the work that builds those connections. Metric spaces are introduced in Chapter 2 as

One of the most powerful concepts in topology. Long defines open covers and subcovers, then contrasts sequential compactness (in metric spaces) with compactness in general spaces. The Heine-Borel theorem is proved as a special case. He also covers the finite intersection property and compact subspaces of Hausdorff spaces. : Essential preliminaries on sets

: Essential preliminaries on sets, functions, and relations that underpin all topological definitions.