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Indian Institute of Science Education and Research Bhopal
MTH 304: Metric Spaces and Topology (4)
Pre-requisites: MTH 303 Real Analysis I
Definition, open sets, closed sets, limit points, convergence, completeness, Baire’s theorem, continuity, spaces of continuous functions
Compactness, sequential compactness, compact metric spaces, compact-open topology, Ascoli’s theorem
Completeness, space filling curve, nowhere differentiable functions
Topology
Definition and examples of topology, base, subbase, weaker and stronger topology
Order topology, subspace topology, product and box topology
Continuity, homeomorphisms, quotient topology
Compact spaces, examples, Tychonoff’s theorem and locally compact spaces, limit point compactness, local compactness
Connected spaces, components, path components, totally disconnected spaces, locally connected spaces, examples
Countability axioms, separation axioms, completely regular and normal spaces, Urysohn’s lemma, Tietze extension theorem, Urysohn embedding theorem, Stone-Cech compacitification
Suggested Books:
- G. F. Simmons, Introduction to Topology and Modern Analysis, Tata McGraw Hill, 2008
- J. R. Munkres, Topology (2nd Edn), Dorling Kindersley, 2006
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