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BY 4.0 license Open Access Published by De Gruyter Open Access December 31, 2020

Ultradiversification of Diversities

Pouya Haghmaram and Kourosh Nourouzi EMAIL logo


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.

MSC 2010: 26E30; 54E40; 54E99


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Received: 2020-03-27
Accepted: 2020-12-08
Published Online: 2020-12-31
Published in Print: 2020-01-01

© 2020 Pouya Haghmaram et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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