Geodesic
A Metrization Theorem for 2-Manifolds
Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 95-104

Voir la notice de l'article provenant de la source Cambridge University Press

There are few known metrization theorems for manifolds (locally Euclidean, connected, Hausdorff space). It is well known that for manifolds metrizability, second countability, Lindelöf's condition, σ-compactness and paracompactness are equivalent. Although these conditions imply separability, the latter does not imply any of the former (see Example 2.2), as is often believed. A common source of metrization for a covering manifold is that lifted from the base manifold [8; p. 181].For 2-manifolds, the presence of a complex analytic structure gives us a metrization theorem; it has been shown [1] that such manifolds are topologically characterized as those which are orientable and second countable. 
Vincent, Paul A. A Metrization Theorem for 2-Manifolds. Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 95-104. doi: 10.4153/CMB-1976-014-x
@article{10_4153_CMB_1976_014_x,
     author = {Vincent, Paul A.},
     title = {A {Metrization} {Theorem} for {2-Manifolds}},
     journal = {Canadian mathematical bulletin},
     pages = {95--104},
     year = {1976},
     volume = {19},
     number = {1},
     doi = {10.4153/CMB-1976-014-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-014-x/}
}
TY  - JOUR
AU  - Vincent, Paul A.
TI  - A Metrization Theorem for 2-Manifolds
JO  - Canadian mathematical bulletin
PY  - 1976
SP  - 95
EP  - 104
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-014-x/
DO  - 10.4153/CMB-1976-014-x
ID  - 10_4153_CMB_1976_014_x
ER  - 
%0 Journal Article
%A Vincent, Paul A.
%T A Metrization Theorem for 2-Manifolds
%J Canadian mathematical bulletin
%D 1976
%P 95-104
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-014-x/
%R 10.4153/CMB-1976-014-x
%F 10_4153_CMB_1976_014_x

[1] 1. Ahlfors, L. V. and Sario, L., Riemann Surfaces, Princeton Univ. Press, Princeton, N.J., 1960. Google Scholar

[2] 2. Calabi, E. and Rosenlicht, M., Complex analytic manifolds without countable base, Proc. Amer. Math. Soc. 4 (1953), 335–340. Google Scholar

[3] 3. Cannon, R. J. Quasiconformal structures and the metrization of 2-manifolds, Trans. Amer. Math. Soc, Vol. 135(1969), 95–103. Google Scholar

[4] 4. Jenkins, J., Univalent Functions and Conformai Mapping, Springer-Verlag, Berlin, 1958. Google Scholar

[5] 5. Jenkins, J. and Morse, M., The existence of pseudoconjugates on Riemann surfaces, Fund. Math. 39 (1952) 269–287. Google Scholar

[6] 6. Jenkins, J. and Morse, M., Topological methods on Riemann surfaces, Annals of Math. Studies, No. 30, 111–139. Princeton, 1953. Google Scholar

[7] 7. Jenkins, J. and Morse, M., Conjugate nets on an open Riemann surface, Lectures on Functions of a Complex Variable, ed. Kaplan, W. et al., 123–185. The University of Michigan Press, 1955. Google Scholar

[8] 8. Massey, W., Algebraic Topology: An Introduction, Harcourt, Brace and World, Inc., New York, 1967. Google Scholar

[9] 9. Stoilow, S., Principles Topologiques de la Théorie des Fonctions Analytiques, Paris, Gauthiers-Villars, 2nd ed., 1956. Google Scholar

[10] 10. Vincent, P., Families of Generalized Continua on 2-manifolds, Ph.D. Thesis, University of Rochester, 1973. Google Scholar

Cité par Sources :