π-METRIZABLE SPACES AND STRONGLY p-METRIZABLE SPACES

摘要

A space X is said to be 7r-metrizable if it has a ovdjscrete p-base. In this paper, we mainly give affirmative answers for two questions about p-metrizable spaces. The main results are that: (1) A space X is p-metrizable if and only if X has a a-hereditarily closure-preserving 7r-base; (2) X is 7r.-metrizable if and only if X is almost s-paracompact and lo-cally 7r-metrizable; (3) Open and closed maps preserve 7r-metrizability; (4) 7r-metrizability satisfies hereditarily closure-preserving regular closed sum theorems. Moreover, we define the notions of second-countable 7r-metrizable and strongly p-metrizable spaces, and study some related questions. Some questions about strongly 7r-metrizability are posed.