A Course on Borel Sets by S. M. Srivastava (auth.)

By S. M. Srivastava (auth.)

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R, by (i) and (ii) we have I/(x} - h(y)/d(y, A)I :5 f. 21 Let X and A be as in the last theorem and J ~ IR an interval. Show that every continuous I : A --+ J admits a continuous extension F : X --+ J. 22 Let X be metrizable, A ~ X closed and K ~ IR n a closed, bounded, and convex set. Show that every continuous function I from A to K admits a continuous extension to X. 1 Metric 47 Sp~ A real-valued map I defined on a metric space X is called uppersemicontinuous (lower-semicontlnuous) if for every real number a, the set {x EX: I(x) ~ a} ({x EX: I(x) ~ a}) is closed.

Let A e F. 1'}. (ii) Fq ~ A(F}. Let (An) be a sequence in F. For (SO,S1,'" ,Sm-1) e N

A tree T on A is a nonempty subset of A

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