Aggarwal N. General Topology 2022

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Aggarwal N. General Topology 2022

Textbook in PDF format Topology is that branch of mathematics which deals with the study of those properties of certain objects that remain invariant under certain kind of transformations as bending or stretching. In simple words, topology is the study of continuity and connectivity. Topology, like other branches of pure mathematics, is an axiomatic subject. In this, we use a set of axioms to prove propositions and theorems. Topological Spaces. Basis for Topology. The Order Topology. The Product Topology on X × Y. The Subspace Topology. Closed Sets and Limit Point. Continuous Functions. The Product Topology. The Metric Topology. The Quotient Topology. Connected Spaces, Connected Subspaces of Real Line. Components and Local Connectedness. Compact Spaces and Compact Subspace of Real Line. Limit Point Compactness. Local Compactness. The Countability Axioms. The Separation Axioms. Normal Spaces, Regular Spaces and Completely Regular Spaces. The Urysohn Lemma. Urysohn Metrization Theorem. The Tietze Extension Theorem. The Tychonoff Theorem. The Stone-Cech Compactification. Local Finiteness and Paracompactness. The Nagata-Smirnov Metrization Theorem. The Smirnov Metrization Theorem. Complete Metric Spaces. Compactness in Metric Spaces. Pointwise and Compact Convergence. Ascoli’s Theorem. Baire Spaces. Introduction to Dimension Theory