A Note on Secuence-Covering Images of Metric Spaces

Abstract

In this brief note, we prove that every space is a sequence-covering image of a topological sum of convergent sequences. As the application of this result, sequence-covering images of locally compact metric spaces (or, locally separable metric spaces, metric spaces) and sequentially-quotient images of a locally compact metric spaces (or, locally separable metric spaces, metric spaces) are equivalent.