Lipschitz retraction of finite subsets of Hilbert spaces

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.

Specializes the result from v1 to Hilbert spaces. The problem remains open for general Hadamard spaces

References in corpus (3)

• Lipschitz extension of multiple Banach-valued functions in the sense of Almgren
• A new proof of the Lie-Trotter-Kato formula in Hadamard spaces
• Symmetric products of the line: embeddings and retractions

Cited by in corpus (4)

• Lipschitz clustering in metric spaces
• Lipschitz retractions in Hadamard spaces via gradient flow semigroups
• On Lipschitz Retraction of Finite Subsets of Normed Spaces
• Anti-absorbing ternary operations on metric spaces