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Connected Convex Subsets

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Let A and B be separated subsets of some Rk, suppose and , and define

for . Put , . [Thus if and only if .]

(a) Prove that Ao and Bo are separated subsets of R1 .
(b) Prove that there exists such that .
(c) Prove that every convex subset of Rk is connected


Solution Summary

Connected convex subsets are investigated.