Cantor's intersection theorem: Difference between revisions

Revision as of 11:08, 22 December 2021

Revision as of 20:47, 16 February 2022

Line 3:

==Topological Statement==

'''Theorem.''' ''Let <math>S</math> be a [[Topological Space|topological space]]. A decreasing nested sequence of non-empty compact, closed subsets of <math>S</math> has a non-empty intersection. In other words, supposing <math>(C_k)_{k \geq 0}</math> is a sequence of non-empty compact subsets of S satisfying''

:<math>C_0 \supset C_1 \supset \cdots \supset C_n \supset C_{n+1} \supset \cdots, </math>