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Semi-Continuous Function on a Compact Subset

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Show that if f is an upper semi-continuous function on a compact subset K of R^p with values in R, then f is bounded above and attains its supremum on K.

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R^p--Let p be a natural number and let R^p denote the collection of all ordered "p-tuples"---i.e. (x_1, x_2,..., x_p) with x_i being a real number

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It is shown that if f is an upper semi-continuous function on a compact subset K of R^p with values in R, then f is bounded above and attains its supremum on K. The solution is detailed and well presented.

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