## Abstract

We prove an equivariant version of the classical Menger-Nöbeling theorem regarding topological embeddings: Whenever a group G acts on a finite-dimensional compact metric space X, a generic continuous equivariant function from X into ([0,1]r)^{G} is a topological embedding, provided that for every positive integer N the space of points in X with orbit size at most N has topological dimension strictly less than rN2. We emphasize that the result imposes no restrictions whatsoever on the acting group G (beyond the existence of an action on a finite-dimensional space). Moreover if G is finitely generated then there exists a finite subset F⊂G so that for a generic continuous map h:X→[0,1]^{r}, the map h^{F}:X→([0,1]r)^{F} given by x↦(f(gx))_{g∈F} is an embedding. This constitutes a generalization of the Takens delay embedding theorem into the topological category.

Original language | American English |
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Journal | Mathematische Annalen |

DOIs | |

State | Accepted/In press - 1 Jan 2024 |

## All Science Journal Classification (ASJC) codes

- General Mathematics