MathDB
Miklos Schweitzer 1981_9

Source:

January 31, 2009
topology

Problem Statement

Let n≥2 n \geq 2 be an integer, and let X X be a connected Hausdorff space such that every point of X X has a neighborhood homeomorphic to the Euclidean space Rn \mathbb{R}^n. Suppose that any discrete (not necessarily closed ) subspace D D of X X can be covered by a family of pairwise disjoint, open sets of X X so that each of these open sets contains precisely one element of D D. Prove that X X is a union of at most ℵ1 \aleph_1 compact subspaces. Z. Balogh
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