PARAMETRIC BING AND KRASINKIEWICZ MAPS:REVISITED

摘要

Let M be a complete metric ANR-space such that for any met-ric compactum K the function space C(K, M) contains a dense set of Bing (resp., Krasinkiewicz) maps. It is shown that M has the following property: If f : X →Y is a perfect surjection between metric spaces, then C(X, M) with the source limitation topology contains a dense C_δ-subset of maps g such that all restrictions g|f~(-1)(y), y ∈Y, are Bing (resp., Krasinkiewicz) maps. We apply the above result to establish some mapping theorems for extensional dimension.