Tchebycheff Approximation and Related Extremal Problems
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA MATHEMATICS RESEARCH LAB
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One of the principal maneuvers available for proving existence theorems is to establish that the desired point is where a continuous real-valued function achieves an extremum on a compact set. If the extremum sought is an infimum, then the functional need only be lower semicontinuous. The crux of an existence proof along these lines would then be the definition of an appropriate topology in which the functional is lower semicontinuous and the set compact.
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