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Proceedings of the American Mathematical Society

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A sequential property of $ \mathsf {C}_p(X)$
and a covering property of Hurewicz


Author: Marion Scheepers
Journal: Proc. Amer. Math. Soc. 125 (1997), 2789-2795
MSC (1991): Primary 54E99
DOI: https://doi.org/10.1090/S0002-9939-97-03897-5
MathSciNet review: 1396994
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Abstract: $\mathsf {C}_p(X)$ has the monotonic sequence selection property if there is for each $f$, and for every sequence $(\sigma _n:n<\omega )$ where for each $n$ $\sigma _n$ is a sequence converging pointwise monotonically to $f$, a sequence $(f_n:n<\omega )$ such that for each $n$ $f_n$ is a term of $\sigma _n$, and $(f_n:n<\omega )$ converges pointwise to $f$. We prove a theorem which implies for metric spaces $X$ that $\mathsf {C}_p(X)$ has the monotonic sequence selection property if, and only if, $X$ has a covering property of Hurewicz.


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Additional Information

Marion Scheepers
Affiliation: Department of Mathematics Boise State University Boise, Idaho 83725
Email: marion@math.idbsu.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03897-5
Keywords: Countable fan tightness, countable strong fan tightness, strong Fr\'echet property, $\gamma$-set, Hurewicz property, Lusin set, Menger property, Rothberger property, Sierpi\'nski set, $\mathsf{S}_1(\Gamma, \Gamma ), \mathfrak{b}, \mathsf{cov}(\mathcal{M}), \mathfrak{d}, \mathfrak{p}$
Received by editor(s): December 15, 1995
Received by editor(s) in revised form: April 11, 1996
Additional Notes: The author’s research was supported in part by NSF grant DMS 95 - 05375.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society