- E10
[0VP] Topics:compact.Prerequisites:[0V6].
Let \((X,d)\) be a metric space, and let \(A_ n⊆ X\) be compact non-empty subsets such that \(A_{n+1}⊆ A_ n\): then \(⋂_{n∈ℕ} A_ n≠ ∅\).
(This result can be derived from [0J6]; but try to give a direct demonstration, using the characterization of ”compact” as ”sequentially compact ”, i.e. the first point in [0V3]).
Solution 1
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English
Authors:
"Mennucci , Andrea C. G."
.
Bibliography
Book index
Book index
- Cantor, intersection theorem
- intersection theorem , see Cantor, intersection theorem
- theorem, intersection --- , see Cantor, intersection theorem
- compact set
- metric space
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