### Around Ulam's question on retractions

#### Abstract

It is known that the unit ball in infinitely dimensional Hilbert space can be retracted onto its boundary via a lipschitzian mapping. The magnitude of Lipschitz constant is only roughly estimated. The note contains a number of observations connected to this result and opens some new problems.

#### Keywords

Lipschtz mappings; optimal retractions on sphere

#### Full Text:

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