COMPACT-COVERING AND 1-SEQUENCE-COVERING IMAGES OF METRIC SPACES

摘要

In this paper, compact-covering and 1-sequence-covering images of metric spaces are investigates. By a Ponomarev's system, this paper characterizes sn-metrizable spaces by 1-sequence-covering, compact-covering and mssc-images of metric spaces, and it is proved that a space X has a point-star network consisting of locally finite sn-covers if and only if X is a sequence-covering, pi and sigma-image of a metric space. As an application of these results, this paper gives an affirmative answer to a question posed by P. Yan and S. Lin in Chinese Adv. Math.