On PCF spaces which are not Frechet-Urysohn

Juan Carlos Martínez

Abstrakt

By means of a forcing argument, it was shown by Pereira that if CH holds then there is a separable PCF space of height ω1 + 1 which is not Fréchet-Urysohn. In this paper, we give a direct proof of Pereira’s theorem by means of a forcing-free argument, and we extend his result to PCF spaces of any height δ + 1 where δ<ω2 with cf(δ) = ω1.

Received 12 June 2017

Research supported by the Spanish Ministry of Education DGI grant MTM2014-59178-P and by the Catalan DURSI grant 2014SGR437.

AMS subject classification: 03E35, 03E04, 03E75, 06E05, 54A25, 54G12

Słowa kluczowe: PCF space, Sequentiality, Fréchet-Urysohn property
References

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