While the goal of general topology is to move beyond distance, connecting abstract topologies back to metric spaces is highly instructional. Long details how any metric (distance formula) naturally induces a topology, and discusses the concept of —determining when an abstract topological space can be given a metric. Why Study Paul E. Long's Approach?
: The book heavily encourages mathematical maturity. Readers are expected to actively engage with proofs rather than passively skimming examples. an introduction to general topology paul e long pdf link
This brings us to the core of your search: While the goal of general topology is to
Searching for "An Introduction to General Topology" Paul E. Long filetype:pdf on Google or academic search engines may yield previews or legally hosted instructor copies, but be cautious of copyright infringement. Using library services is always safer, legal, and often more reliable than random PDF links. Long's Approach
The famous hierarchy: ( T_0, T_1, T_2 ) (Hausdorff), regular (( T_3 )), and normal (( T_4 )) spaces. Long explains why Hausdorff spaces are essential for uniqueness of limits and why normal spaces are required for Urysohn’s metrization theorem (introduced later in exercises).