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Topological aspects of the space of metric measure spaces

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Abstract

Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several topological properties on the space equipped with these distance functions toward a deep understanding of convergence theory.

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Acknowledgements

The authors thank Professors Takumi Yokota and Yoshito Ishiki for their valuable comments. The authors would like to thank an anonymous referee for carefully reading the manuscript and for his/her valuable comments.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan

    Daisuke Kazukawa

  2. Mathematical Sciences Course, Ehime University, Matsuyama, 790-8577, Japan

    Hiroki Nakajima

  3. Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

    Takashi Shioya

Authors
  1. Daisuke Kazukawa
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  2. Hiroki Nakajima
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  3. Takashi Shioya
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Correspondence to Daisuke Kazukawa.

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This work was supported by JSPS KAKENHI Grant Number JP22K20338, JP22K13908, JP19K03459.

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Kazukawa, D., Nakajima, H. & Shioya, T. Topological aspects of the space of metric measure spaces. Geom Dedicata 218, 68 (2024). https://doi.org/10.1007/s10711-024-00921-3

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