Previous |  Up |  Next

Article

Title: Productively Fréchet spaces (English)
Author: Jordan, Francis
Author: Mynard, Frédéric
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 54
Issue: 4
Year: 2004
Pages: 981-990
Summary lang: English
.
Category: math
.
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. (English)
Keyword: Fréchet
Keyword: strongly Fréchet filters and spaces
Keyword: product spaces
MSC: 54A20
MSC: 54B10
MSC: 54D55
MSC: 54D99
MSC: 54G20
idZBL: Zbl 1080.54506
idMR: MR2100010
.
Date available: 2009-09-24T11:19:33Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/127946
.
Reference: [1] A.  Arhangel’skiĭ: The frequency spectrum of a topological space and the product operation.Trans. Moscow Math. Soc. 40 (1981), 163–200.
Reference: [2] C. Costantini and P. Simon: An $\alpha _4$, not Fréchet product of $\alpha _4$ Fréchet spaces.Topology Appl. 108 (2000), 43–52. MR 1783423, 10.1016/S0166-8641(00)90096-8
Reference: [3] S. Dolecki: Convergence-theoretic methods in quotient quest.Topology Appl. 73 (1996), 1–21. MR 1413721, 10.1016/0166-8641(96)00067-3
Reference: [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
Reference: [5] S. Dolecki and F. Mynard: Convergence-theoretic mechanism behind product theorems.Topology Appl. 104 (2000), 67–99. MR 1780899, 10.1016/S0166-8641(99)00012-7
Reference: [6] S. Dolecki and T. Nogura: Two-fold theorem on Fréchetness of products.Czechoslovak Math. J. 49 (1999), 421–429. MR 1692508, 10.1023/A:1022420806729
Reference: [7] E. van Douwen: The product of a Fréchet space and a metrizable space.Topology Appl. 47 (1992), 163–164. Zbl 0759.54013, MR 1192305, 10.1016/0166-8641(92)90026-V
Reference: [8] J. Gerlits and Z. Nagy: On Fréchet spaces.Rend. Circ. Mat. Palermo (2) 18 (1988), 51–71. MR 0958724
Reference: [9] G. Gruenhage: A note on the product of Fréchet spaces.Topology Proc. 3 (1979), 109–115. Zbl 0427.54017, MR 0540482
Reference: [10] C. Kendrick: On product of Fréchet spaces.Math. Nachr. 65 (1975), 117–123. 10.1002/mana.19750650109
Reference: [11] I. Labuda: Compactoidness in topological spaces.(to appear).
Reference: [12] V. I. Malyhin: On countable spaces having no bicompactification of countable tightness.Dokl. Akad. Nauk SSR 206 (6) (1972), 1407–1411. Zbl 0263.54015, MR 0320981
Reference: [13] E. Michael: A quintuple quotient quest.Gen. Topology Appl. 2 (1972), 91–138. Zbl 0238.54009, MR 0309045, 10.1016/0016-660X(72)90040-2
Reference: [14] F. Mynard: Coreflectively modified continuous duality applied to classical product theorems.Applied Gen. Top. 2 (2001), 119–154. Zbl 1007.54008, MR 1890032
Reference: [15] P. Nyikos: Subsets of $\omega ^{\omega }$ and the Fréchet-Urysohn and $\alpha _i$-properties.Topology Appl. 48 (1992), 91–116. MR 1195504, 10.1016/0166-8641(92)90021-Q
Reference: [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
Reference: [17] T. Nogura: A counterexample for a problem of Arhangel’skiĭ concerning the Product of Fréchet spaces.Topology Appl. 25 (1987), 75–80. MR 0874979, 10.1016/0166-8641(87)90076-9
Reference: [18] J. Novák: Double convergence and products of Fréchet spaces.Czechoslovak Math. J. 48 (1998), 207–227. MR 1624303, 10.1023/A:1022829218525
Reference: [19] J. Novák: A note on product of Fréchet spaces.Czechoslovak Math. J. 47 (1997), 337–340. 10.1023/A:1022877814524
Reference: [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
Reference: [21] R. C. Olson: Biquotient maps, countably bisequential spaces and related topics.Topology Appl. 4 (1974), 1–28. MR 0365463, 10.1016/0016-660X(74)90002-6
Reference: [22] P. Simon: A compact Fréchet space whose square is not Fréchet.Comment. Math. Univ. Carolin. 21 (1980), 749–753. Zbl 0466.54022, MR 0597764
Reference: [23] K. Tamano: Product of compact Fréchet spaces.Proc. Japan Acad. Ser. A. Math. Sci. 62 (1986), 304–307. MR 0868827, 10.3792/pjaa.62.304
Reference: [24] S. Todorcevic: Some applications of S and L combinatorics.Annals New York Acad. Sci., 1991, pp. 130–167. MR 1277886
.

Files

Files Size Format View
CzechMathJ_54-2004-4_14.pdf 370.1Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo