Abstract:We provide proper mapping-characterizations of some embedding-like properties weaker than P ! -embedding. For instance, we show that a subset A of a space X is U ! -embedded in X if and only if for every continuous map g: A ! Y into a Banach space Y of weight w(Y) r !, there exists a continuous set-valued mapping ' of X into the nonempty compact subsets of Y such that g is a selection for ' j A (i.e., g(x) 2 '(x) for every x 2 A). On the other hand, we show that a subset A is C*-embedded in X if and only if fo… Show more
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