Regular networks for metrizable spaces and Lasnev spaces

• Autorzy: Sakai M. , Tamano K. , Yajima Y.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Frechet; HCP-regular; k-network; Lasnev space; LF-regular; metrizable

PL

topologia

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no 2
• Strony: 121--133
• Opis fizyczny: Bibliogr. 17 poz.,

Twórcy

autor

Sakai M.

autor

Tamano K.

autor

Yajima Y.