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QUESTION
Suppose K1, . , Kd are compact subsets of R. Prove that K1 K2 Kd := {(x1, . , xd) R^d: xi Ki i {1, . , d}} is a compact subset of R d .
Suppose K1, . . . , Kd are compact subsets of R. Prove that K1 × K2 × · · · × Kd := {(x1, . . . , xd) ∈ R^d: xi ∈ Ki ∀ i ∈ {1, . . . , d}} is a compact subset of Rd.
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