Universal spaces for finite-dimensional closed images of locally compact metric spaces

For each nonnegative integer n, we show the existence of a universal space for the class of all at most n-dimensional closed images of locally compact separable metric spaces. For the construction, we use some properties of universal Menger compacta and a construction of UVn-maps due to Ferry. We also discuss the nonseparable cases under a certain condition on the weight of metric spaces.