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.

• Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan (MS)

autor

Tamano K.

• Faculty of Engineering, Yokohama National University, Yokohama 240-8801, Japan (Kt)

autor

Yajima Y.

• Department Of Mathematics, Kanagawa University, Yokohama 221-8686, Japan (Yy) e-mail:

Bibliografia

• [1] P. S. Alexandroff, On the metrization of topodogical spaces, Bull. Acad.Polon. Sci., Ser. Sci. Math., 8 (1960) 135-140.
• [2] A. V. Arhangel`skii, Onthe metrization of topoloqical spaces, Bull. Acad. Polon. Sci., Ser. Sci. Math., 8 (1960) 589-595. -[3] Н. J. К. Junnila, Y. Yajinia, Normality and countable paracompactness with σ-spaces having speciad nets, Topology Appl., to be published.
• [4] R. Engelking, Geneтad Topology, PWN, Warszawa 1977.
• [5] E. Мichael, A quintuple quotient quest, Gen. Тороlоgy Appl., 2 (1972) 91- 138
• [6] G. Gruenhage, E. Michael, Y. Tanaka, Spaces determined by point-cоuntаblе covers, Pacific J. Math., 113 (1984) 303-332.
• [7] R. W. Heath On spaces with, point-contable bases, Bull. Acad. Polon. Sci., Ser. Sci. Math., 13 (1965) 393-395.
• [8] R. W. Heath, D. J. Lutzer, P. L. Zenor, Monotonnically normal spaces, Trans. Amer. Math. Soc., 178 (1973) 481-493.
• [9] D. K. Burke, R. Engelking, D. J. Lutzer, Hereditarily closure- preserving collections and metrization, Proc. Amer. Math. Soc., 51 (1975) 483-488.
• [10] L. Foged, A countable k-space that is not stratifable, Proc. Amer. Math. Sос., 81 (1981) 337-338.
• [11] D. K. Burk e, E. Мichael, On. certain point-countable covers, Pacific J. Math.. 64 (1976) 79-92.
• [12] L. Foged, A characterization of closed images of metric spaces, Proc. Amer. Math. Soc., 95 (1985) 487-490.
• [13] Y. Tanaka., Point-countable covers and k-networks, Tоpоlоgy Proc., 12 (1987) 327--349.
• [14] N. Lašnev, Continnous decompositions and closed nnuappings of metric spaces, Soviet Math. Dokl 6 (1965) 1.504-1506.
• [15] Y. Tanaka, H. Zhou, Spaces dominated by metric subsets, Тоpоlоgу Proc., 9 (1984) 149-163.
• [16] C. Liu, Y. Tanaka, Spaces with a star-countable k-network, and related results, Topology Appl., 74 (1996) 25-38.
• [17] М. Sakai, On spaces with a star-countable k-network, Houston J. Math., 23 (1997) 45-56.