On a problem of Nogura about the product of Fréchet-Urysohn 〈 α 4 〉 -spaces

Camillo Costantini

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 3, page 537-549
  • ISSN: 0010-2628

Abstract

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Assuming Martin’s Axiom, we provide an example of two Fréchet-Urysohn 〈 α 4 〉 -spaces, whose product is a non-Fréchet-Urysohn 〈 α 4 〉 -space. This gives a consistent negative answer to a question raised by T. Nogura.

How to cite

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Costantini, Camillo. "On a problem of Nogura about the product of Fréchet-Urysohn $\langle \alpha _4\rangle $-spaces." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 537-549. <http://eudml.org/doc/248392>.

@article{Costantini1999,
abstract = {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.},
author = {Costantini, Camillo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Fréchet-Urysohn space; $\langle \alpha _4\rangle $-space; Martin’s Axiom; almost disjoint functions; double iterated power; Fréchet-Uryson space; -space; Martin's Axiom},
language = {eng},
number = {3},
pages = {537-549},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a problem of Nogura about the product of Fréchet-Urysohn $\langle \alpha _4\rangle $-spaces},
url = {http://eudml.org/doc/248392},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Costantini, Camillo
TI - On a problem of Nogura about the product of Fréchet-Urysohn $\langle \alpha _4\rangle $-spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 537
EP - 549
AB - 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.
LA - eng
KW - Fréchet-Urysohn space; $\langle \alpha _4\rangle $-space; Martin’s Axiom; almost disjoint functions; double iterated power; Fréchet-Uryson space; -space; Martin's Axiom
UR - http://eudml.org/doc/248392
ER -

References

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  2. Arhangel'skii A.V., The frequency spectrum of a topological space and the product operation, Transl. Moscow Math. Soc., Issue 2 (1981), 163-200. (1981) 
  3. Costantini C., Simon P., An α 4 , not Fréchet product of α 4 Fréchet spaces, Topology Appl., to appear. Zbl0959.54006MR1783423
  4. Dow A., Two classes of Fréchet-Urysohn spaces, Proc. Amer. Math. Soc. 108 (1990), 241-247. (1990) Zbl0675.54029MR0975638
  5. Engelking R., General Topology. Revised and Completed Ed., Heldermann, Berlin, 1989. MR1039321
  6. Kunen K., Set Theory. An Introduction to Independence Proofs, Nort-Holland, Amsterdam, 1980. Zbl0534.03026MR0597342
  7. Nogura T., The product of α i -spaces Topology Appl., 21 (1985), 251-259. (1985) MR0812643
  8. Olson R.C., Bi-quotient maps, countably bi-sequential spaces, and related topics, Gen. Topology Appl. 4 (1974), 1-28. (1974) Zbl0278.54008MR0365463
  9. Simon P., A compact Fréchet space whose square is not Fréchet, Comment. Math. Univ. Carolinae 21 (1980), 749-753. (1980) Zbl0466.54022MR0597764
  10. Simon P., A hedgehog in a product, Acta Univ. Carolin.-Math. Phys., to appear. Zbl1007.54023MR1696588

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