本文利用了ｃｓ网、序列邻域网、序列开网和弱基的概念，讨论了空间中点正则覆盖，一致覆盖和点有限覆盖的点星网之间的关系．建立了度量空间在几类序列覆盖（紧）映射下象空间的特征，特别地证明了度量空间的序列覆盖（或１序列覆盖）紧映象等价于具有点正则ｃｓ网的空问，回答了Ｔａｎａｋａ等提出的一个问题．

In this paper authors use the concepts of cs-networks, sequential-neighbor- hood networks, sequential-open networks and weak bases, discuss the relations among point-regular covers, uniform covers and point-star networks of point-finite covers in spaces, and establish the characterizations of images of metric spaces under some sequence-covering (compact) mappings. In particular, it is shown that the image of metric spaces under sequence-covering (or 1-sequence-covering) compact mappings is equivalent to the space with point-regular cs-networks, which answers a Tanaka's question.