Bi-quotient maps and cartesian products of quotient maps
Annales de l'Institut Fourier, Volume 18 (1968) no. 2, p. 287-302

Dans ce travail, on introduit une nouvelle classe d’applications, qui semble avoir beaucoup de propriétés désirables. En particulier, cette classe permet de donner une caractérisation des applications dont le produit cartésien avec une application quotient quelconque est toujours une application quotient.

@article{AIF_1968__18_2_287_0,
     author = {Michael, Ernest},
     title = {Bi-quotient maps and cartesian products of quotient maps},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {18},
     number = {2},
     year = {1968},
     pages = {287-302},
     doi = {10.5802/aif.301},
     zbl = {0175.19704},
     mrnumber = {39 \#6277},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1968__18_2_287_0}
}
Michael, Ernest. Bi-quotient maps and cartesian products of quotient maps. Annales de l'Institut Fourier, Volume 18 (1968) no. 2, pp. 287-302. doi : 10.5802/aif.301. http://www.numdam.org/item/AIF_1968__18_2_287_0/

[1] A. Arhangel'Skiĭ, On a class of spaces containing all metric and all locally bi-compact spaces, Dokl. Akad. Nauk SSSR, 151 (1963), 751-754. (= Soviet Math. Dokl., 4 (1963), 1051-1055). | MR 27 #2959 | Zbl 0124.15801

[2] A. Arhangel'Skiῐ, Some types of factor mappings, and the relations between classes of topological spaces, Dokl. Akad. Nauk SSSR, 153 (1963), 743-746. (= Soviet Math. Dokl, 4 (1963), 1726-1729). | Zbl 0129.38103

[3] A. Arhangel'Skiῐ, Mappings and spaces, Uspehi Mat. Nauk, 21 (1966), 133-184 (= Russian Math. Surveys, 21 (1966), 115-162). | Zbl 0171.43603

[4] N. Bourbaki, Topologie générale, Chapters 1 and 2, Hermann, 1961. | Zbl 0102.37603

[5] R. Brown, Ten topologies for X × Y, Quart. J. Math. Oxford Ser., (2) 14 (1963), 303-319. | MR 28 #2516 | Zbl 0113.37504

[6] R. Brown, Function spaces and product topologies, Quart. J. Math. Oxford Ser., (2) 15 (1964), 238-250. | MR 29 #2779 | Zbl 0126.38503

[7] D. E. Cohen, Spaces with weak topology, Quart. J. Math., Oxford Ser., (2) 5 (1954), 77-80. | MR 16,62c | Zbl 0055.16103

[8] E. Hewitt, A problem of set-theoretic topology, Duke Math. J., 10 (1943), 309-333. | MR 5,46e | Zbl 0060.39407

[9] S. P. Franklin, Spaces in which sequences suffice, Fund. Math., 57 (1965), 107-115. | MR 31 #5184 | Zbl 0132.17802

[10] S. P. Franklin, Spaces in which sequences suffice II, Fund. Math., 61 (1967), 51-56. | MR 36 #5882 | Zbl 0168.43502

[11] E. Michael, A note on closed maps and compact sets, Israel J. Math., 2 (1964), 173-176. | MR 31 #1659 | Zbl 0136.19303

[12] E. Michael, Local compactness and cartesian products of quotient maps and k-spaces, (is printed just before this paper). | Numdam | Zbl 0175.19703

[13] J. Milnor, Construction of universal bundles I, Ann. of Math., 63 (1956), 272-284. | MR 17,994b | Zbl 0071.17302

[14] K. Morita, On decomposition spaces of locally compact spaces, Proc. Japan Acad., 32 (1956), 544-548. | MR 19,49d | Zbl 0072.40402

[15] N. Steenrod, A convenient category of topological spaces, Michigan Math. J., 14 (1967), 133-152. | MR 35 #970 | Zbl 0145.43002

[16] A. H. Stone, Metrisability of decomposition spaces, Proc. Amer. Math. Soc., 7 (1956), 690-700. | MR 19,299b | Zbl 0071.16001

[17] J. H. C. Whitehead, A note on a theorem of Borsuk, Bull. Amer. Math. Soc., 54 (1948), 1125-1132. | MR 10,617c | Zbl 0041.31901