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Fréchet-Urysohn property of quasicontinuous functions
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Abstract
The aim of this paper is to study the Fréchet-Urysohn property of the space Qp(X,R) of real-valued quasicontinuous functions, defined on a Hausdorff space X, endowed with the pointwise convergence topology.
It is proved that under Suslin's Hypothesis, for an open Whyburn space X, the space Qp(X,R) is Fréchet-Urysohn if and only if X is countable. In particular, it is true in the class of first-countable regular spaces X.
In ZFC, it is proved that for a metrizable space X, the space Qp(X,R) is Fréchet-Urysohn if and only if X is countable.
2010 MSC: 54C35, 54C40
Title: Fréchet-Urysohn property of quasicontinuous functions
Description:
Abstract
The aim of this paper is to study the Fréchet-Urysohn property of the space Qp(X,R) of real-valued quasicontinuous functions, defined on a Hausdorff space X, endowed with the pointwise convergence topology.
It is proved that under Suslin's Hypothesis, for an open Whyburn space X, the space Qp(X,R) is Fréchet-Urysohn if and only if X is countable.
In particular, it is true in the class of first-countable regular spaces X.
In ZFC, it is proved that for a metrizable space X, the space Qp(X,R) is Fréchet-Urysohn if and only if X is countable.
2010 MSC: 54C35, 54C40.
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