Self-maps under the compact-open topology
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- 作者：Richard J. Lupton richard.lupton@gmail.com" class="auth_mail" title="E-mail the corresponding author ; Max F. Pitz max.f.pitz@gmail.com" class="auth_mail" title="E-mail the corresponding author
- 关键词：primary ; 54C35 ; secondary ; 54D35 ; 54G05 ; 54E52
- 刊名：Topology and its Applications
- 出版年：2016
- 出版时间：1 October 2016
- 年：2016
- 卷：212
- 期：Complete
- 页码：122-141
- 全文大小：483 K
文摘
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.