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Lecture 34 | Continuity and Compactness | Continuous functions on compact spaces | Analysis | Tamil
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* Definition of bounded functions.
* Continuous image of a compact set (metric space) is compact with proof.
* Continuous real valued function on compact sets attains its maximum and minimum.
* Continuous function on compact set into R^k is bounded.
* If f is a one-one, onto, continuous function defined on compact set, then its inverse is continuous.
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* Reference book: Walter Rudin, Principles of Mathematical Analysis (Third edition).
* For PG students studying "Analysis I".
* Especially for M.Sc. Mathematics (First semester) students under Manonmaniam Sundaranar University (M S University), Tirunelveli.
* Useful for SET/NET/GATE/other competitive examinations.
* Continuous image of a compact set (metric space) is compact with proof.
* Continuous real valued function on compact sets attains its maximum and minimum.
* Continuous function on compact set into R^k is bounded.
* If f is a one-one, onto, continuous function defined on compact set, then its inverse is continuous.
================================================
* Reference book: Walter Rudin, Principles of Mathematical Analysis (Third edition).
* For PG students studying "Analysis I".
* Especially for M.Sc. Mathematics (First semester) students under Manonmaniam Sundaranar University (M S University), Tirunelveli.
* Useful for SET/NET/GATE/other competitive examinations.
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