WebEmeritus Professor of Mathematics Differential Topology. James Munkres served on the MIT Mathematics Faculty from 1960-2000, and continues as Senior. 정석원 윤곽 … Webc is a topology on X. This topology is called the countable complement topology. Lemma 3. The compact subspaces of X are exactly the finite subspaces. Proof. Suppose A is infinite. Let B = {b 1,b 2,...} be a countable subset of A. Set A n = (X −B)∪{b 1,...,b n}. Note that {A n} is an open covering of A with no finite subcovering.

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