An Introduction To General Topology Paul E Long Pdf Link Site

"General Topology, also known as point-set topology, is a branch of mathematics that studies the properties of topological spaces. It is a fundamental area of study in mathematics, with applications in analysis, algebra, and geometry.

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• Chapter 1: Preliminaries – Sets, mappings, equivalence relations, countable and uncountable sets.
• Chapter 2: Topological Spaces – Definition via open sets, closed sets, neighborhood systems, and bases (with many concrete examples: metric spaces, discrete/indiscrete, finite complement, and order topologies).
• Chapter 3: Continuity and Homeomorphisms – ε-δ generalization, sequential continuity, open/closed maps.
• Chapter 4: Product and Quotient Spaces – Finite and infinite products (box vs. product topology), identification spaces.
• Chapter 5: Separation Axioms – T0 through T4, Urysohn lemma (stated and used), Tietze extension theorem (briefly).
• Chapter 6: Compactness – Heine-Borel generalization, countable compactness, sequential compactness, Bolzano-Weierstrass property.
• Chapter 7: Connectedness – Connected and path-connected components, local connectedness.
• Chapter 8: Completeness (in metric spaces) – Completion of a metric space, Baire category theorem.