Asap Let K be a compact subset of a metric space (X, d) and assume that thefunction f K→ R¹ is lower semicontinuous. That isf(xo) lim inf f(x)x→x0Show that(a) m = infek f(x) is finite.(b) There exists € K, so that f(x) = m.Hint: For part a), arguing by contradiction will produce a sequence{n} CK, so that f(n) <-n. For part b), consider a sequence yn, so thatm≤ f(yn) < m + 1/ / .

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Answered: Let K be a compact subset of a metric…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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