130 9 Prove: If S is compact, and f is continuous on S, then f takes a minimum value some-where in S.

Since S is compact and f is continuous, f[S] is a compact subset of R and therefore closed and…

Answered: Prove: If S is compact, and f is…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 16E: Prove that if a subring R of an integral domain D contains the unity element of D, then R is an...

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Prove: If S is compact, and f is continuous on S, then f takes a minimum value some- where in S.