Countable product of function spaces having p-Frechet-Urysohn like properties
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概要
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We exhibit in this article some classes of spaces for which properties γ and γp are countable additive, and we prove that for some type of spaces and ultrafilters p∈ω*, γ is equivalent to γp. We obtain: (1) If {Xn}n<ω is a sequence of metrizable locally compact spaces with γp (p∈ω*), then Пn<ωCπ(Xn) is a FU(p)-space; (2) Cπ(X) os a Frechet-Urysohn (resp., FU(p)) space iff Cπ(F(X)) has the same property, where F(X) is the free topological rroup generated by X; (3) For a locally compact metrizable and non countable space X, Cπ(X) is a Frechet-Uryshon (reso., FU(p)), where Lπ(X) is the dual space of Cπ(X); (4) for every Cech-complete space X and every p∈ω* for which R dose not have γp, Cπ(X) is Frechet-Uryshon iff Cπ(X) is a FU(p)-space. Also we give some results soncerning P-points in ω* related with p-Frechet-Uryshon property and topological function space.
- 筑波大学の論文
- 1997-01-10