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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Regular covers and metrization

Lin S.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 4

427-432

In this paper it is showed that a regular and k-space with a regular k-network is metrizable, which generalized related results of A. Archangielskiĭ, H. W. Martin, M. Sakai, K. Tamano and Y. Yajima.

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.