Michał Popławski

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math.GN2026

Topological size of the set of universal and ultrahomogeneous retractions on the Urysohn space

Judyta Bąk, Joanna Garbulińska-Węgrzyn, Michał Popławski

In this paper, we investigate the set $U (U)$ of universal and ultrahomogeneous $1$ -Lipschitz retractions acting on the Urysohn space as the subspace of the space…

math.GN2024

All iterated function systems are Lipschitz up to an equivalent metric

Michał Popławski

A finite family $F = {f_{1}, \dots, f_{n}}$ of continuous selfmaps of a given metric space $X$ is called an iterated function system (shortly IFS). In a case of contractive se…

math.GN2024

Characterizing Lipschitz images of injective metric spaces

Judyta Bąk, Taras Banakh, Joanna Garbulińska-Węgrzyn +2

A metric space $X$ is {\em injective} if every non-expanding map $f : B \to X$ defined on a subspace $B$ of a metric space $A$ can be extended to a non-expanding map $f ˉ : A \to X$ .…