Self-maps under the compact-open topology

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