Lebl-Basic-Analysis-I · Problem 7.4.10

Metric Spaces

Mathematics · compactness

Problem

Suppose (X,d)(X, d) is complete and suppose we have a countably infinite collection of nonempty compact sets E1⊃E2⊃E3⊃⋯E_1 \supset E_2 \supset E_3 \supset \cdots. Prove ⋂j=1∞Ej≠∅\bigcap_{j=1}^\infty E_j \neq \emptyset.

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