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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). an introduction to general topology paul e long pdf link
If you're looking for a downloadable PDF of the book, you can try searching online academic databases or websites that host free e-books, such as: Used copies are often inexpensive
This brings us to the core of your search: T_2 ) (Hausdorff)
Paul E. Long's An Introduction to General Topology is a classic foundational textbook first published in 1971 as part of the Merrill Mathematics Series