Abstract
In this paper, we give the mapping theorems on \(\aleph\)-spaces and g-metrizable spaces by means of some sequence-covering mappings, mssc-mappings and π-mappings.
Similar content being viewed by others
References
A. Arkhangel'skii: Mappings and spaces. Russian Math. Surveys 21 (1966), 115–162.
S. Lin: Locally countable collections, locally finite collections and Alexandroff's problems. Acta Math. Sinica 37 (1994), 491–496. (In Chinese.)
S. Lin: Generalized Metric Spaces and Mappings. Chinese Scientific publ., Beijing, 1995.
L. Foged: Characterizations of \(\aleph\)-spaces. Pacific J. Math. 110 (1984), 59–63.
J. Nagata: General metric spaces I. In: Topics in General Topology. North-Holland, Amsterdam, 1989.
F. Siwiec: Sequence-covering and countably bi-quotient mappings. Gen. Top. Appl. 1 (1971), 143–154.
Y. Tanaka: Symmetric spaces, g-developable spaces and g-metrizable spaces. Math. Japonica 36 (1991), 71–84.
F. Siwiec: On defining a space by a weak-base. Pacific J. Math. 52 (1974), 233–245.
G. Gruenhage, E. Michael and Y. Tanaka: Spaces determined by point-countable covers. Pacific J. Math. 113 (1984), 303–332.
V. I. Ponomarev: Axioms of countability and continuous mappings. Bull. Pol. Acad. Math. 8 (1960), 127–133.
P. O'Meara: On paracompactness in function spaces with the compact-open topology. Proc. Amer. Math. Soc. 29 (1971), 183–189.
R. W. Heath: On open mappings and certain spaces satisfying the first countability axiom. Fund. Math. 57 (1965), 91–96.
J. A. Kofner: On a new class of spaces and some problems of symmetrizability theory. Soviet Math. Dokl. 10 (1969), 845–848.
D. K. Burke: Cauchy sequences in semimetric spaces. Proc. Amer. Math. Soc. 33 (1972), 161–164.
K. B. Lee: On certain g-first countable spaces. Pacific J. Math. 65 (1976), 113–118.
L. Foged: On g-metrizability. Pacific J. Math. 98 (1982), 327–332.
S. Lin: A note on the Arens' space and sequential fan. Topology Appl. 81 (1997), 185–196.
S. Lin: On g-metrizable spaces. Chinese Ann. Math. 13 (1992), 403–409.
C. Liu and M. Dai: g-metrizability and S ω. Topology Appl. 60 (1994), 185–189.
Y. Tanaka: σ-hereditarily closure-preserving k-networks and g-metrizability. Proc. Amer. Math. Soc. 112 (1991), 283–290.
R. H. Bing: Metrization of topological spaces. Canad. J. Math. 3 (1951), 175–186.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Li, S. A Note on \(\aleph\)-Spaces and g-Metrizable Spaces. Czech Math J 55, 803–808 (2005). https://doi.org/10.1007/s10587-005-0066-1
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10587-005-0066-1