Lipschitz retraction of finite subsets of Hilbert spaces

Leonid V. Kovalev

doi:10.1017/s0004972715000672

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arXiv · 1406.6742

Lipschitz retraction of finite subsets of Hilbert spaces

Leonid V. Kovalev

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Abstract

Finite subset spaces of a metric space $X$ form a nested sequence under natural isometric embeddings $X=X(1)\subset X(2)\subset\dots$. We prove that this sequence admits Lipschitz retractions $X(n)\to X(n-1)$ when $X$ is a Hilbert space.

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BibTeX RIS

Leonid V. Kovalev. 2015-04-19. Lipschitz retraction of finite subsets of Hilbert spaces. https://doi.org/10.1017/s0004972715000672

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