Sequence-covering maps of metric spaces

Let f : X --> Y be a map, f is a sequence-covering map if whenever {y(n)} is a convergent sequence in Y, there is a convergent sequence {x(n)} in X with each x(n) is an element of f(-1)(y(n)). f is a 1-sequence-covering map if for each y is an element of Y, there is x is an element of f(-1)(y) such that whenever {y(n)} is a sequence converging to y in Y there is a sequence {x(n)} converging to x in X with each x(n) is an element of f(-1)(y(n)). In this paper we investigate the structure of sequence-covering images of metric spaces, the main results are that (1) every sequence-covering, quotient and s-image of a locally separable metric space is a local N-0-space; (2) every sequence-covering and compact map of a metric space is a 1-sequence-covering map. (C) 2001 Elsevier Science B.V. All rights reserved.