# Article

Full entry | PDF   (0.2 MB)
Keywords:
Fréchet-Urysohn space; $\langle\alpha_4\rangle$-space; Martin's Axiom; almost disjoint functions; double iterated power
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.
References:
[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
[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.
[CS] Costantini C., Simon P.: An $\alpha_4$, not Fréchet product of $\alpha_4$ Fréchet spaces. Topology Appl., to appear. MR 1783423 | Zbl 0959.54006
[Do] Dow A.: Two classes of Fréchet-Urysohn spaces. Proc. Amer. Math. Soc. 108 (1990), 241-247. MR 0975638 | Zbl 0675.54029
[En] Engelking R.: General Topology. Revised and Completed Ed. Heldermann, Berlin, 1989. MR 1039321
[Ku] Kunen K.: Set Theory. An Introduction to Independence Proofs. Nort-Holland, Amsterdam, 1980. MR 0597342 | Zbl 0534.03026
[No] Nogura T.: The product of $\left\langle\alpha_i\right\rangle$-spaces Topology Appl. 21 (1985), 251-259. MR 0812643
[Ol] Olson R.C.: Bi-quotient maps, countably bi-sequential spaces, and related topics. Gen. Topology Appl. 4 (1974), 1-28. MR 0365463 | Zbl 0278.54008
[Si1] Simon P.: A compact Fréchet space whose square is not Fréchet. Comment. Math. Univ. Carolinae 21 (1980), 749-753. MR 0597764 | Zbl 0466.54022
[Si2] Simon P.: A hedgehog in a product. Acta Univ. Carolin.-Math. Phys., to appear. MR 1696588 | Zbl 1007.54023

Partner of