This paper investigates the space
w the MathML source">Ck(ω⁎,ω⁎), the space of continuous self-maps on the Stone–Čech remainder of the integers,
w the MathML source">ω⁎, equipped
with the compact-open topology. Our main results are that
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w the MathML source">Ck(ω⁎,ω⁎) is Baire,
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Stone–Čech extensions of injective maps on ω form a dense set of weak P -points in w the MathML source">Ck(ω⁎,ω⁎),
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it is independent of ZFC whether w the MathML source">Ck(ω⁎,ω⁎) contains P-points, and that
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w the MathML source">Ck(ω⁎,ω⁎) is not an F -space, but contains, as w the MathML source">ω⁎, no non-trivial convergent sequences.