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arXiv · 2309.08786

The radius of comparison of $C (X)$

N. Christopher Phillips
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Abstract

Let X be a compact Hausdorff space. Then the radius of comparison rc ( C (X)) is related to the covering dimension dim (X) by rc ( C (X)) \geq [ dim (X) - 7 ] / 2. Except for the additive constant, this improves a result of Elliott and Niu, who proved that if X is metrizable then rc (C (X)) \geq [ dim_{\mathbb{Q}} (X) - 4 ] / 2. There are compact metric spaces X for which the estimate of Elliott and Niu gives no information, but for which rc ( C (X)) is infinite or has arbitrarily large finite values.

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N. Christopher Phillips. 2023-09-15. The radius of comparison of $C (X)$. https://arxiv.org/abs/2309.08786

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