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