Previous |  Up |  Next


Title: On a problem of Nogura about the product of Fréchet-Urysohn $\langle \alpha_4\rangle$-spaces (English)
Author: Costantini, Camillo
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 40
Issue: 3
Year: 1999
Pages: 537-549
Category: math
Summary: Assuming Martin's Axiom, we provide an example of two Fréchet-Urysohn $\langle\alpha_4\rangle$-spaces, whose product is a non-Fréchet-Urysohn $\langle\alpha_4\rangle$-space. This gives a consistent negative answer to a question raised by T. Nogura. (English)
Keyword: Fréchet-Urysohn space
Keyword: $\langle\alpha_4\rangle$-space
Keyword: Martin's Axiom
Keyword: almost disjoint functions
Keyword: double iterated power
MSC: 03E50
MSC: 54A20
MSC: 54A35
MSC: 54B10
MSC: 54D55
MSC: 54D80
MSC: 54G15
MSC: 54G20
idZBL: Zbl 1010.54041
idMR: MR1732482
Date available: 2009-01-08T18:55:04Z
Last updated: 2012-04-30
Stable URL:
Reference: [Ar1] Arhangel'skii A.V.: The frequency spectrum of a topological space and the classification of spaces.Sov. Math. Dokl. 13 (1972), 265-268. MR 0394575
Reference: [Ar2] Arhangel'skii A.V.: The frequency spectrum of a topological space and the product operation.Transl. Moscow Math. Soc., Issue 2 (1981), 163-200.
Reference: [CS] Costantini C., Simon P.: An $\alpha_4$, not Fréchet product of $\alpha_4$ Fréchet spaces.Topology Appl., to appear. Zbl 0959.54006, MR 1783423
Reference: [Do] Dow A.: Two classes of Fréchet-Urysohn spaces.Proc. Amer. Math. Soc. 108 (1990), 241-247. Zbl 0675.54029, MR 0975638
Reference: [En] Engelking R.: General Topology. Revised and Completed Ed..Heldermann, Berlin, 1989. MR 1039321
Reference: [Ku] Kunen K.: Set Theory. An Introduction to Independence Proofs.Nort-Holland, Amsterdam, 1980. Zbl 0534.03026, MR 0597342
Reference: [No] Nogura T.: The product of $\left\langle\alpha_i\right\rangle$-spaces Topology Appl..21 (1985), 251-259. MR 0812643
Reference: [Ol] Olson R.C.: Bi-quotient maps, countably bi-sequential spaces, and related topics.Gen. Topology Appl. 4 (1974), 1-28. Zbl 0278.54008, MR 0365463
Reference: [Si1] Simon P.: A compact Fréchet space whose square is not Fréchet.Comment. Math. Univ. Carolinae 21 (1980), 749-753. Zbl 0466.54022, MR 0597764
Reference: [Si2] Simon P.: A hedgehog in a product.Acta Univ. Carolin.-Math. Phys., to appear. Zbl 1007.54023, MR 1696588


Files Size Format View
CommentatMathUnivCarolRetro_40-1999-3_13.pdf 274.0Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo