Continua in the Gromov–Hausdorff space

نویسندگان

چکیده

We first prove that for all compact metrizable spaces, there exists a topological embedding of the space into each sets metric spaces which are connected, path-connected, geodesic, or CAT(0), in Gromov–Hausdorff with finite prescribed values. As its application, we show above path-connected and their non-empty open subsets have infinite dimension. By same method, also set proper CAT(0) is dimension respect to pointed distance.

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ژورنال

عنوان ژورنال: Topology and its Applications

سال: 2022

ISSN: ['1879-3207', '0166-8641']

DOI: https://doi.org/10.1016/j.topol.2022.108058