Continuity and Compactness on R (Part 2) | Real Analysis | B.Sc./B.A. (Mathematics) Third Year, TU

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Kshitiz Mangal Bajracharya

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Published on August 29, 2024 4:37:19 PM ● Video Link: https://www.youtube.com/watch?v=FK391yHrnuI

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In this video, we prove that if f: A $\rightarrow$ R is continuous with A being compact, then the function f is closed. This covers second half of the proof of the statement "continuous image of a compact set is compact". The method used here, however, should NOT be replicated for general metric spaces.

A brief discussion of the fact that a real-valued continuous function attains its maximum and minimum values provided that its domain is compact is also included at the end.

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