## Details of MA3201 (Spring 2020)

Level: 3 |
Type: Theory |
Credits: 4.0 |

Course Code | Course Name | Instructor(s) |
---|---|---|

MA3201 |
Topology |
Soumalya Joardar |

Syllabus |
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Metric Spaces: Metric space topology, equivalent metrics, sequences, complete metric spaces, limits and continuity, uniform continuity, extension of uniformly continuous functions.
Topological Spaces: Definition, examples, bases, sub-bases, product topology, subspace topology, metric topology, quotient topology, second countability and separability. Continuity: Continuous functions on topological spaces, homeomorphisms. Connectedness: Definition, example, path connectedness and local connectedness. Compactness: Definition, limit point compactness, sequential compactness, net and directed set, local compactness, Tychonoff theorem, Stone-Weierstrass theorem, Arzela-Ascoli theorem. Topological Groups: Definitions, examples, compactness and connectedness in matrix groups. Separation Axioms: Hausdorff, regular and normal spaces; Urysohn lemma and Tietze extension theorem; compactification. Metrizability: Urysohn metrization theorem. |

Prerequisite |
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Analysis III (MA3101) and Algebra I (MA3102). |

References |
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. Armstrong, M.A., Basic Topology, Springer-Verlag
2. Dugundji, J., Topology, Allyn and Bacon Series in Advanced Mathematics, Allyn & Bacon. 3. Kelley, J.L., General Topology, Springer-Verlag. 4. Munkres, J.R., Topology (2nd Edition), Prentice-Hall. 5 Simmons, G.F., Introduction to Topology and Modern Analysis, Tata McGraw-Hill |

#### Course Credit Options

Sl. No. | Programme | Semester No | Course Choice |
---|---|---|---|

1 | IP | 2 | Core |

2 | IP | 4 | Not Allowed |

3 | IP | 6 | Not Allowed |

4 | MR | 2 | Not Allowed |

5 | MR | 4 | Not Allowed |

6 | MS | 6 | Core |

7 | RS | 1 | Not Allowed |

8 | RS | 2 | Not Allowed |