Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Fréchet; strongly Fréchet filters and spaces; product spaces
Fréchet; strongly Fréchet filters and spaces; product spaces
Summary:
We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.
References:
[1] A. Arhangel’skiĭ: The frequency spectrum of a topological space and the product operation. Trans. Moscow Math. Soc. 40 (1981), 163–200.
[2] C. Costantini and P. Simon: An $\alpha _4$, not Fréchet product of $\alpha _4$ Fréchet spaces. Topology Appl. 108 (2000), 43–52. DOI 10.1016/S0166-8641(00)90096-8 | MR 1783423
[3] S. Dolecki: Convergence-theoretic methods in quotient quest. Topology Appl. 73 (1996), 1–21. DOI 10.1016/0166-8641(96)00067-3 | MR 1413721
[4] S. Dolecki: Active boundaries of upper semi-continuous and compactoid relations closed and inductively perfect maps. Rostock Math. Coll. 54 (2000), 51–68. MR 1820118
[5] S. Dolecki and F. Mynard: Convergence-theoretic mechanism behind product theorems. Topology Appl. 104 (2000), 67–99. DOI 10.1016/S0166-8641(99)00012-7 | MR 1780899
[6] S. Dolecki and T. Nogura: Two-fold theorem on Fréchetness of products. Czechoslovak Math. J. 49 (1999), 421–429. DOI 10.1023/A:1022420806729 | MR 1692508
[7] E. van Douwen: The product of a Fréchet space and a metrizable space. Topology Appl. 47 (1992), 163–164. DOI 10.1016/0166-8641(92)90026-V | MR 1192305 | Zbl 0759.54013
[8] J. Gerlits and Z. Nagy: On Fréchet spaces. Rend. Circ. Mat. Palermo (2) 18 (1988), 51–71. MR 0958724
[9] G. Gruenhage: A note on the product of Fréchet spaces. Topology Proc. 3 (1979), 109–115. MR 0540482 | Zbl 0427.54017
[10] C. Kendrick: On product of Fréchet spaces. Math. Nachr. 65 (1975), 117–123. DOI 10.1002/mana.19750650109
[11] I. Labuda: Compactoidness in topological spaces. (to appear).
[12] V. I. Malyhin: On countable spaces having no bicompactification of countable tightness. Dokl. Akad. Nauk SSR 206 (6) (1972), 1407–1411. MR 0320981 | Zbl 0263.54015
[13] E. Michael: A quintuple quotient quest. Gen. Topology Appl. 2 (1972), 91–138. DOI 10.1016/0016-660X(72)90040-2 | MR 0309045 | Zbl 0238.54009
[14] F. Mynard: Coreflectively modified continuous duality applied to classical product theorems. Applied Gen. Top. 2 (2001), 119–154. MR 1890032 | Zbl 1007.54008
[15] P. Nyikos: Subsets of $\omega ^{\omega }$ and the Fréchet-Urysohn and $\alpha _i$-properties. Topology Appl. 48 (1992), 91–116. DOI 10.1016/0166-8641(92)90021-Q | MR 1195504
[16] T. Nogura: Product of Fréchet spaces. General Topology and its relations to modern analysis and algebra VI. Proc. Prague Topological Sympos. 86 (1988), 371–378. MR 0952623
[17] T. Nogura: A counterexample for a problem of Arhangel’skiĭ concerning the Product of Fréchet spaces. Topology Appl. 25 (1987), 75–80. DOI 10.1016/0166-8641(87)90076-9 | MR 0874979
[18] J. Novák: Double convergence and products of Fréchet spaces. Czechoslovak Math. J. 48 (1998), 207–227. DOI 10.1023/A:1022829218525 | MR 1624303
[19] J. Novák: A note on product of Fréchet spaces. Czechoslovak Math. J. 47 (1997), 337–340. DOI 10.1023/A:1022877814524
[20] J. Novák: 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. MR 0474222
[21] R. C. Olson: Biquotient maps, countably bisequential spaces and related topics. Topology Appl. 4 (1974), 1–28. DOI 10.1016/0016-660X(74)90002-6 | MR 0365463
[22] P. Simon: A compact Fréchet space whose square is not Fréchet. Comment. Math. Univ. Carolin. 21 (1980), 749–753. MR 0597764 | Zbl 0466.54022
[23] K. Tamano: Product of compact Fréchet spaces. Proc. Japan Acad. Ser. A. Math. Sci. 62 (1986), 304–307. DOI 10.3792/pjaa.62.304 | MR 0868827
[24] S. Todorcevic: Some applications of S and L combinatorics. Annals New York Acad. Sci., 1991, pp. 130–167. MR 1277886
Search
Partner of
