Two infinite versions of nonlinear Dvoretzky's theorem

TL;DR

This paper explores two infinite variants of the nonlinear Dvoretzky's theorem, focusing on countably infinite metric spaces and analytic sets with infinite Hausdorff dimension, expanding the theorem's scope.

Contribution

It introduces two new infinite versions of the nonlinear Dvoretzky's theorem applicable to infinite metric spaces and sets with infinite Hausdorff dimension.

Findings

Established nonlinear Dvoretzky's theorem for countably infinite metric spaces.

Extended the theorem to analytic sets with infinite Hausdorff dimension.

Abstract

We investigate nonlinear Dvoretzky's theorem for countably infinite metric spaces and analytic sets whose Hausdorff dimension are infinite.