The Ramsey property for C
p
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Authors: | M Sakai |
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Institution: | 1. Department of Mathematics, Kanagawa University, Yokohama, 221-8686, Japan
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Abstract: | For a Tychonoff space X, we denote by C p (X) the space of real-valued continuous functions with the topology of pointwise convergence. We show that (a) Arhangel℉skii℉s property (α 2) and the Ramsey property introduced by Nogura and Shakhmatov are equivalent for C p (X), (b) the Ramsey property and Nyikos’ property (α 3/2) are not equivalent for C p (X). These results answer questions posed by Shakhmatov. Concerning properties (α i ) for C p (X), some results on Scheepers’ conjecture are also given. |
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