On free spaces

Abstract

A continuum is a connected, compact, metric space. A continuum is decomposable if it is a union of two proper subcontinua. A continuum is indecomposable if it is not decomposable. A continuum is hereditarily indecomposable if each of its subcontinua is indecomposable. A space is called a Bing space if each of its components is a hereditarily indecomposable continuum. A map is a continuous function. A map is called a Bing map if each of its fibers is a Bing space. In 1958, Brown constructed a Bing map from 'Rn' - {0} to 'R'. In 1996, Levin proved that the set of Bing maps is a dense G[delta]-subset of 'C'('X, I') (or 'C'('X, R')) for any compactum ' X'. Krasinkiewicz proved the same result for the case of ' n'-dimensional manifolds 'M' ('n'