Question

(A generalization of the nested interval theorem) Suppose {Sk} is a sequence of nonempty compact suubsets of Rn such that S1 ⊃ S2 ⊃ §3 ⊃ . . .. Show that ∩ ∞ k=1Sk 6= φ. (This can be done with either the Bolzano-Weierstrass theorem of the Heine-Borel theorem. Can you find both proofs?)

Answer 1