Two classes of Fréchet-Urysohn spaces

Author:
Alan Dow

Journal:
Proc. Amer. Math. Soc. **108** (1990), 241-247

MSC:
Primary 54E35; Secondary 03E35, 03E75, 54A35

MathSciNet review:
975638

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Abstract: Arhangel'skii introduced five classes of spaces, -spaces , which are important in the study of products of Fréchet-Urysohn spaces. For each , each -space is an -space and it follows from the continuum hypothesis that there are countable -spaces which are not -spaces. A -space (-space) is a Fréchet-Urysohn -space ( -space). We show that there is a model of set theory in which each -space (-space) is an -space (-space).

**[A1]**A. V. Arhangel′skiĭ,*Frequency spectrum of a topological space and classification of spaces*, Dokl. Akad. Nauk SSSR**206**(1972), 265–268 (Russian). MR**0394575****[A2]**-,*The frequency spectrum of a topological space and the product operation*, Trudy Mosk. Mat. Obs.**40**(1979) = Transl. Moscow Math. Soc. (1981), Issue 2, 163-200.**[DS]**A. Dow and J. Steprans.**[G]**Gary Gruenhage,*Infinite games and generalizations of first-countable spaces*, General Topology and Appl.**6**(1976), no. 3, 339–352. MR**0413049****[L]**Richard Laver,*On the consistency of Borel’s conjecture*, Acta Math.**137**(1976), no. 3-4, 151–169. MR**0422027****[LNy]**R. Levy and P. Nyikos,*Families in**whose union is regular open*, preprint.**[N]**Tsugunori Nogura,*A counterexample for a problem of Arhangel′skiĭ concerning the product of Fréchet spaces*, Topology Appl.**25**(1987), no. 1, 75–80. MR**874979**, 10.1016/0166-8641(87)90076-9**[Ny1]**P. Nyikos,*and the Fréchet-Urysohn property*, in preparation.**[Ny2]**-,*The Cantor tree and the Fréchet-Urysohn property*, preprint, 1987.**[O]**Roy C. Olson,*Bi-quotient maps, countably bi-sequential spaces, and related topics*, General Topology and Appl.**4**(1974), 1–28. MR**0365463****[S1]**Saharon Shelah,*Proper forcing*, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin-New York, 1982. MR**675955****[S2]**-,*Cardinal invariants of the continuum*, Axiomatic Set Theory, Eds. J. Baumgartner, D. A. Martin, S. Shelah, Contemp. Math. Amer. Math. Soc., Providence, R.I., 1986.**[Sh]**P. L. Sharma,*Some characterizations of 𝑊-spaces and 𝑤-spaces*, General Topology Appl.**9**(1978), no. 3, 289–293. MR**510910**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-0975638-7

Keywords:
Fréchet-Urysohn space,
-space,
-space

Article copyright:
© Copyright 1990
American Mathematical Society