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arXiv · 2208.00962

Topological and metric emergence of continuous maps

Maria Carvalho·Fagner B. Rodrigues·Paulo Varandas
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Abstract

We prove that the homeomorphisms of a compact manifold with dimension one have zero topological emergence, whereas in dimension greater than one the topological emergence of a C^0-generic conservative homeomorphism is maximal, equal to the dimension of the manifold. Moreover, we show that the metric emergence of continuous self-maps on compact metric spaces has the intermediate value property.

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Maria Carvalho, Fagner B. Rodrigues, Paulo Varandas. 2022-08-01. Topological and metric emergence of continuous maps. https://doi.org/10.1017/s0305004124000343

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