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Real analysis: Compact Space and Infimum

Assume that f is a continuous real valued function on the compact space X, then show there exists a point x-bar E X such that f(x-bar)=inf{f(x): x E X) .


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Compact space and infimum are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.