Cardinalities of metric completions

Ronald Freiwald

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Given a topological property P, we study when it reflects in small continuous images, i.e., when for some infinite cardinal κ, a space X has P if and only if all its continuous images of weight less or equal to κ have P. We say that a cardinal invariant η reflects in continuous images of weight κ + if η(X) ≤ κ provided that η(Y) ≤ κ whenever Y is a continuous image of X of weight less or equal to κ +. We establish that, for any infinite cardinal κ, the spread, character, pseudocharacter...