A note on Collins-Roscoe Structuring Mechanism

2014/08/19 by Ziqin Feng, Feng, Ziqin
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.GN

paper · pdf · doi:10.48550/arxiv.1408.4436

This paper has been withdrawn by the author due to a crucial error

arxiv created 2018/05/16 · arxiv updated 2018/05/17

Abstract

A space X has countable (F)-property if it has countable point network satisfying the Collins-Roscoe structuring mechanism. Some sufficient conditions for C_p(X) having countable (F)-property are obtained. As a corollary, we prove that if X is Corson compact, C_p(X) satisfies countable (F). This answers a question raised by Tkachuk. Also we get a class of function spaces with hereditarily D-property. We also prove that the countable (F)-property is preserved by taking Σ_s-product. This answers questions of Tkachuk positively.

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