A note on Collins-Roscoe Structuring Mechanism

Ziqin Feng

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arXiv · 1408.4436

A note on Collins-Roscoe Structuring Mechanism

Ziqin Feng

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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 $\Sigma_s$-product. This answers questions of Tkachuk positively.

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Ziqin Feng. 2014-08-19. A note on Collins-Roscoe Structuring Mechanism. https://arxiv.org/abs/1408.4436

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