Les espaces topologiques dont le produit avec chaque espace fortement de Fréchet est de Fréchet sont caractérisés de façon interne. Ceci résout un problème resté longtemps ouvert.
The class of topological spaces whose product with every strongly Fréchet space is also Fréchet is characterized internally. This solves a long standing problem.
Accepté le :
Publié le :
Francis Jordan 1 ; Frédéric Mynard 1
@article{CRMATH_2002__335_3_259_0,
author = {Francis Jordan and Fr\'ed\'eric Mynard},
title = {Espaces productivement de {Fr\'echet}},
journal = {Comptes Rendus. Math\'ematique},
pages = {259--262},
publisher = {Elsevier},
volume = {335},
number = {3},
year = {2002},
doi = {10.1016/S1631-073X(02)02473-1},
language = {fr},
}
Francis Jordan; Frédéric Mynard. Espaces productivement de Fréchet. Comptes Rendus. Mathématique, Volume 335 (2002) no. 3, pp. 259-262. doi : 10.1016/S1631-073X(02)02473-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02473-1/
[1] The frequency spectrum of a topological space and the product operation, Trans. Moscow Math. Soc., Volume 40 (1981), pp. 163-200
[2] An α4, not Fréchet product of α4 Fréchet spaces, Topology Appl., Volume 108 (2000) no. 1, pp. 43-52
[3] Convergence-theoretic methods in quotient quest, Topology Appl., Volume 73 (1996), pp. 1-21
[4] Active boundaries of upper semi-continuous and compactoid relations; closed and inductively perfect maps, Rostock. Math. Kollog., Volume 54 (2000), pp. 3-20
[5] Two-fold theorem on Fréchetness of products, Czech. Math. J., Volume 49 (1999) no. 2, pp. 421-429
[6] The product of a Fréchet space and a metrizable space, Topology Appl., Volume 47 (1992) no. 3, pp. 163-164
[7] On Fréchet spaces, Rend. Circ. Mat. Palermo (2), Volume 18 (1988), pp. 51-71
[8] A note on the product of Fréchet spaces, Topology Proc., Volume 3 (1979) no. 1, pp. 109-115
[9] On product of Fréchet spaces, Math. Nachr., Volume 65 (1975), pp. 117-123
[10] A quintuple quotient quest, Gen. Topology Appl., Volume 2 (1972), pp. 91-138
[11] Coreflectively modified continuous duality applied to classical product theorems, Appl. Gen. Top., Volume 2 (2001) no. 2, pp. 119-154
[12] Product of Fréchet spaces, General Topology and its Relations to Modern Analysis and Algebra VI, Proc. Prague Topological Sympos., 86, 1988, pp. 371-378
[13] A counterexample for a problem of Arhangel'skiĭ concerning the product of Fréchet spaces, Topology Appl., Volume 25 (1987), pp. 75-80
[14] Double convergence and products of Fréchet spaces, Czech. Math. J., Volume 48 (1998) no. 2, pp. 207-227
[15] A note on product of Fréchet spaces, Czech. Math. J., Volume 47 (1997) no. 2, pp. 337-340
[16] Concerning the topological product of two Fréchet spaces, General Topology and its Relations to Modern Analysis and Algebra IV, Proc. Fourth Prague Topological Sympos., 1977, pp. 342-343
[17] Classes of compact sequential spaces, Set Theory and its Applications, Toronto, ON 1987, Lecture Notes in Math., 1401, 1989, pp. 135-159
[18] Biquotient maps, countably bisequential spaces and related topics, Topology Appl., Volume 4 (1974), pp. 1-28
[19] A compact Fréchet space whose square is not Fréchet, Comment. Math. Univ. Carolin., Volume 21 (1980), pp. 749-753
[20] Product of compact Fréchet spaces, Proc. Japan Acad. Ser. A. Math. Sci., Volume 62 (1986) no. 8, pp. 304-307
Cité par Sources :
Commentaires - Politique