Course Archives Theoretical Statistics and Mathematics Unit  
Course: Topology Level: Undergraduate Time: Currently not offered 

Syllabus Past Exams Syllabus: i) METRIC SPACES: Elements of metric space theory. Sequences and Cauchy sequences and the notion of completeness, elementary topological notions for metric spaces i.e.open sets, closed sets, compact sets, connectedness, continuous and uniformly continuous functions on a metric space. The Bolzano  Weirstrass theorem, Supremum and infimum on compact sets, Rn as a metric space. ii) TOPOLOGICAL SPACES: Definitions and Examples; Bases and subbases; Subspace and metric topology; closed sets, limit points and continuous functions; product and quotient topology. iii) SEPARATION: Countability and Seperation axioms, Normal spaces, Urysohn lemma, Tietze extension theorem. iv) CONNECTEDNESS AND COMPACTNESS: Connected subspaces of the real line, Compact subspaces of the real line, limit point compactness, local compactness. Tychnoffs theorem. One point compactification. Reference Texts: (a) J. Munkres: Topology a first course. (b) M. A. Armstrong: Basic Topology. (c) G. F. Simmons: Introduction to Topology and Modern Analysis. (d) K. Janich: Topology. Top of the page Past Exams  
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[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute] 