Abstract
In this paper, we prove that a space is a strongly g-developable space iff it is a sequence-covering, quotient, π, mssc-image of a metric space, which answers a question for strongly g-developable spaces.
Similar content being viewed by others
References
A. V. Arhangel’skii, Mappings and spaces, Russian Math. Surveys 21, 115 (1966).
R. Engelking, General Topology (revised and completed edition) (Berlin: Heldermann, 1989).
S. P. Franklin, Spaces in which sequence suffice, Fund. Math. 57, 107 (1965).
Y. Ge, Characterizations of sn-metrizable spaces, Publ. Inst. Math. Nouv. Ser. 74(88), 121(2003).
Y. Ge and S. Lin, g-Metrizable spaces and the images of semi-metric spaces, Czech. Math. J. 57, 1141 (2007).
J. A. Guthrie, A characterization of ℵ 0 -spaces, General Topology Appl. 1, 105 (1971).
Y. Ikeda, C. Liu, and Y. Tanaka, Quotient compact images ofmetric spaces, and related matters, Topology Appl. 122, 237 (2002).
Z. Li, On π-s-images of metric spaces, International Journal of Mathematics and Mathematical Sciences 7, 1101 (2005).
S. Lin and P. Yan, Sequence-covering maps of metric spaces, Topology Appl. 109, 301 (2001).
S. Lin and P. Yan, Notes on cfp-covers, Comment Math. Univ. Carolinae 44, 295 (2003).
F. Siwiec, Sequence-covering and countably bi-quotient mappings, General Topology Appl. 1, 143 (1971).
F. Siwiec, On defining a space by a weak base, Pacific J. Math. 52, 233 (1974).
Y. Tanaka, σ-hereditarily closure-preserving k-networks and g-metrizability, Proc. Amer. Math. Soc. 112, 283 (1991).
Y. Tanaka and Y. Ge, Around quotient compact images of metric spaces, and symmetric spaces,Houston J. Math. 32, 99 (2006).
Y. Tanaka and Z. Li, Certain covering-maps and k-networks, and related matters, Topology Proc. 27, 317 (2003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Submitted by M.A. Malakhaltsev
This project is supported by the NSF of China (No. 10971181 and 10971186), the NSF of Hunan Province in China (No. 09JJ6005).
Rights and permissions
About this article
Cite this article
Ge, X., Li, Z. On strongly g-developable spaces. Lobachevskii J Math 31, 60–64 (2010). https://doi.org/10.1134/S1995080210010099
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080210010099