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Abstract
In this paper, we prove, for a space X, the following are equivalent:
1. X is a D1 space with a regular-Gδ-diagonal,
2. X is a D2 space with a regular-Gδ-diagonal,
3. X is a semi-developable space with Gδ (3) -diagonal,
4. X is a D1-space with a Gδ(3)-diagonal,
5. X is a D2 -space with a Gδ(3)-diagonal,
6. X is a q, -space with a G*δ (2)-diagonal,
7. X is a semi-developable space with G*δ (2)-diagonal,
8. X is a semimetrizable, c-stratifiable space,
9. X is a c-Nagata -space,
10. X is a K-semimetrizable.
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References
- ALEXANDER, C.1971. Semi-developable space and quotient images of metric spaces, Pacific J. Math 37: 277-293.
- ARHANGEL'SKII, A. 1966. Mappings and spaces, Russian Math. Surveys, 21:115-162.
- BORGES, C. 1968. On metrizability of topological spaces, Canad. J. Math. 20:795-804.
- GITTINGS, R. 1975. On o-semimetrizable space, Studies in topology, Academic Press, New York, 179-188.
- GRUENHAGE, G.1984.Generalized metric spaces, Handbook of Set-theoretic Topology 423-501.
- MARTIN, H.W.1973. Metrizability of M-spaces, Canad. J. Math., 25:840-841.
References
ALEXANDER, C.1971. Semi-developable space and quotient images of metric spaces, Pacific J. Math 37: 277-293.
ARHANGEL'SKII, A. 1966. Mappings and spaces, Russian Math. Surveys, 21:115-162.
BORGES, C. 1968. On metrizability of topological spaces, Canad. J. Math. 20:795-804.
GITTINGS, R. 1975. On o-semimetrizable space, Studies in topology, Academic Press, New York, 179-188.
GRUENHAGE, G.1984.Generalized metric spaces, Handbook of Set-theoretic Topology 423-501.
MARTIN, H.W.1973. Metrizability of M-spaces, Canad. J. Math., 25:840-841.