Abstract In this paper, using the idea of ultrametrization of metric spaces we introduce ultradiversification of diversities. We show that every diversity has an ultradiversification which is the greatest nonexpansive ultra-diversity image of it. We also investigate a Hausdorff-Bayod type problem in the setting of diversities, namely, determining what diversities admit a subdominant ultradiversity. This gives a description of all diversities which can be mapped onto ultradiversities by an injective nonexpansive map. The given results generalize similar results in the setting of metric spaces.

中文翻译：

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多样性的超多样化

摘要 在本文中，利用度量空间的超度量化思想，我们引入了多样性的超多样化。我们表明，每一个多样性都有一个超多样化，这是它最大的非扩张性超多样化形象。我们还研究了多样性设置中的 Hausdorff-Bayod 类型问题，即确定哪些多样性承认次要的超多样性。这给出了可以通过内射非膨胀映射映射到超多样性的所有多样性的描述。给定的结果概括了度量空间设置中的类似结果。