Problem 4 (Extending continuous functions). Suppose KC Rm is compact and f: KR" is continuous. Show that there exists a continuous mapping f: Rm Rn such that f = f on K.
Problem 4 (Extending continuous functions). Suppose KC Rm is compact and f: KR" is continuous. Show that there exists a continuous mapping f: Rm Rn such that f = f on K.
Problem 4 (Extending continuous functions). Suppose KC Rm is compact and f: KR" is continuous. Show that there exists a continuous mapping f: Rm Rn such that f = f on K.
Transcribed Image Text:Problem 4 (Extending continuous functions). Suppose KC Rm is compact and
f: K→ R is continuous. Show that there exists a continuous mapping f: Rm Rn such that
f = f on K.
Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
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