Another Approach to Parametric Bing and Krasinkiewicz Maps 1

摘要

Using a factorization theorem due to Pasynkov [11] we provide a short; proof of the existence and density of parametric Bing and Krasinkiewicz maps. In particular, the following corollary is established: Let f: X → Y be a surjective map between paracompact spaces such that all fibers f~(-1)(y), y ∈ Y, are compact and there exists a map g: X→Ⅱ~N_0 embedding each f~(-1)(y) into Ⅱ~N_0. Then for every n ≥ 1 the space C~*(X, R~n) of all bounded continuous functions with the uniform convergence topology contains a dense set of maps g such that any restriction g|f~(-1)(y), y ∈ Y, is a Bing and Krasinkiewicz map.