Geodesic
A Topological Characterization of Conjugate Nets
Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 707-721

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

One aspect of topological analysis that authors, such as G. T. Whyburn and Marston Morse, have pointed to ([16; 6] for instance) as being fundamental in the development of function theory is the topological study of the level sets of analytic and harmonic functions or of their topological analogues, light open maps and pseudo-harmonic functions. The first step in this direction seems to have been made by H. Whitney [14] when he studied families of curves, given abstractly using a condition of regularity. 
Vincent, Paul A. A Topological Characterization of Conjugate Nets. Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 707-721. doi: 10.4153/CJM-1977-075-9
@article{10_4153_CJM_1977_075_9,
     author = {Vincent, Paul A.},
     title = {A {Topological} {Characterization} of {Conjugate} {Nets}},
     journal = {Canadian journal of mathematics},
     pages = {707--721},
     year = {1977},
     volume = {29},
     number = {4},
     doi = {10.4153/CJM-1977-075-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-075-9/}
}
TY  - JOUR
AU  - Vincent, Paul A.
TI  - A Topological Characterization of Conjugate Nets
JO  - Canadian journal of mathematics
PY  - 1977
SP  - 707
EP  - 721
VL  - 29
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-075-9/
DO  - 10.4153/CJM-1977-075-9
ID  - 10_4153_CJM_1977_075_9
ER  - 
%0 Journal Article
%A Vincent, Paul A.
%T A Topological Characterization of Conjugate Nets
%J Canadian journal of mathematics
%D 1977
%P 707-721
%V 29
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-075-9/
%R 10.4153/CJM-1977-075-9
%F 10_4153_CJM_1977_075_9

[1] 1. Anderson, R. D., On monotone interior mappings of the plane, Trans. Amer. Math. Soc. 73 (1952), 211–222. Google Scholar

[2] 2. Boothby, W. M., The topology of regular curve families with multiple saddle points, Amer. J. Math. 73 (1951), 405–438. Google Scholar

[3] 3. Boothby, W. M. The topology of level curves of harmonic functions with critical points, Amer. J. Math. 73 (1951), 512–538. Google Scholar

[4] 4. Fox, W. C., The critical points of peano-interior functions defined on 2-manifolds, Trans. Amer. Math. Soc. 83 (1956), 338–370. Google Scholar

[5] 5. Hocking, J. G. and Young, G. S., Topology (Addison-Wesley, Reading, Mass., 1961). Google Scholar

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

[7] 7. Jenkins, J. and Morse, M. Topological methods on Riemann surfaces, Annals of Math. Studies, 30 111–139 (Princeton, 1953). Google Scholar

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

[9] 9. Kaplan, W., Regular curve families filling the plane, Duke Math. Jour. 7 (1940) 154-185; 8 (1941), 11–45. Google Scholar

[10] 10. Moore, R. L., Foundations of point set theory, Amer. Math. Soc. Colloquium Publications 13 (1932). Google Scholar

[11] 11. Roberts, J. H., Concerning collections of continua not all bounded, Amer. J. Math. 52 (1930), 551–562. Google Scholar

[12] 12. Rutt, N. E., On certain types of plane continua, Trans. Amer. Math. Soc. 33 (1931), 806–816. Google Scholar

[13] 13. Vincent, P., A metrization theorem for 2-manifolds, Can. Math. Bull. 19 (1976), 95–104. Google Scholar

[14] 14. Whitney, H., Regular families of curves, Ann. of Math. 34 (1933), 244–270. Google Scholar

[15] 15. Whyburn, G. T., Analytic topology, Amer. Math. Soc. Colloquium Publications, 28, New York, 1942. Google Scholar

[16] 16. Whyburn, G. T. Continuous decompositions, Amer. Jour. Math. 71 (1949), 218–226. Google Scholar

Cité par Sources :