关于sn-度量空间

本文利用ｓｎ－度量空间的一些等价刻划及ｓｎ－度量空间与ｇ－度量空间、度量空间之间的关系，研究了ｓｎ－度量空间的一些映射性质，证明了ｓｎ－度量空间的闭象是ｓｎ－度量空间当且仅当它是ｓｎ－第一可数的，利用这一结果证明了有限到一闭映射和开闭映射均保持ｓｎ－度量空间，并给出反例说明完备映射不保持ｓｎ－度量空间，本文还证明了ｓｎ－变量空问满足完备逆象Ｇδ－对角线定理．

On sn-Metrizable Spaces

In this paper, we investigate some closed mappings properties on sn-metri- zable spaces by using the characterizations of sn-metrizable spaces and the relations among sn-metrizable spaces, g-metrizable spaces and metrizable spaces. We prove that the closed image of a sn-metrizable space is sn-metrizable if it is sn-first countable. By this result, we prove that the finite-to-one closed mappings and the open-closed mappings preserve sn-metrizable spaces, and give a counterexample to show that the perfect mappings do not preserve, sn-metrizable spaces. In addition, we prove that sn-metrizable spaces satisfy the perfect inverse image Cδ-diagonal theorem.