## Iwao Yoshioka

*On spaces with point-countable $k$-systems *

Comment.Math.Univ.Carolinae 45,4 (2004) 749-765. **Abstract:**This paper deals with the behavior of $M$-spaces, countably bi-quasi-$k$-spaces and singly bi-quasi-$k$-spaces with point-countable $k$-systems. For example, we show that every $M$-space with a point-countable $k$-system is locally compact paracompact, and every separable singly bi-quasi-$k$-space with a point-countable $k$-system has a countable $k$-system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael's paper [15] when the spaces have point-countable $k$-systems.

**Keywords:** countably-bi-quasi-$k$-space, point-countable $k$-system, local compactness, \newline metrizability

**AMS Subject Classification:** 54D55, 54E18, 54E35

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