Course Archives Theoretical Statistics and Mathematics Unit
Course: Topology
Instructor: Maneesh Thakur
Room: G26
Level: Undergraduate
Time: Currently 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 sub-bases; 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.

Evaluation:
Mid-Term 30 marks
Assignment 20 marks
Final Exam 50 marks
Total 100 marks


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Past Exams

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