Prove if s is finite set then s is a convex and compact set

Reference no: EM131330310

1. Prove that if S is a finite set then (S) is a convex and compact set.

2. Let A ⊆ Rⁿ and B ⊆ R^m be two compact sets. Prove that the product set A × B ⊆ R^n+m is a compact set.

3. Let A ⊆ Rⁿ and B ⊆ R^m be two convex sets. Prove that the product set A × B ⊆ R^n+m is a convex set.

Reference no: EM131330310

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