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

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

$\mathsf {C}(X)$ 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 …