局部可数集族、局部有限集族与Alexandroff问题

Locally Countable Collections, Locally Finite Collections and Alexandroff's Problems

本文引进分层强ｓ－映射和分层强紧映射建立具有σ－局部可数网、具有σ－局部可数ｋ－网、具有σ－局部可数基的正则空间以及σ－空间、－空间、ｇ－可度量空间和确定的度量空间之间的联系．这些都是对Ａｌｅｘａｎｄｒｏｆｆ问题的回答．

In this paper, stratified strong s-mappings and stratified strong compact mappings are introduced, by which the relations between matrizable, spaces and spaces with σ-locally countable networks, or spaces with σ-locally countable k-networks, or spaces with σ-locally countable bases, or σ-spaces, or -spaces, or g-metrizable spaces are established. Those are some answers to Alexandroff's problems.