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Cofinal families of compacta in separable metric spaces

Author: Fons van Engelen
Journal: Proc. Amer. Math. Soc. 104 (1988), 1271-1273
MSC: Primary 54H05
MathSciNet review: 969060
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Abstract: We show that if $ X$ is a $ \Pi _1^1$-set, then the family of compact subsets of $ X$ contains a cofinal (w.r.t. inclusion) subset of cardinality $ {\mathbf{d}}$; the same is true if $ X$ is $ \Pi _3^1$, under strong set-theoretic hypotheses.

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