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Regular networks for metrizable spaces and Lasnev spaces

Sakai M., Tamano K., Yajima Y.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 2

121-133

In 1960, Arhangel'skii gave a metrization theorem, showing that a space is metrizable if and only if it has a regular base. In the present paper, we prove two metrization theorems analogous tu Arhangel'skii's. For these two, we make use of regular k-networks and generalized regular bases, called HCP-regular bases, respectively. Next, we give a characterization of Lasnev spaces, using HCP-regular networks. Moreover, we give a partial answer to a problem concerning Lasnev spaces and regular networks, raised by Junnila and Yajima.