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# Homology, Homotopy and Applications

## Volume 9 (2007)

### Number 1

### Classification of di-embeddings of the $n$-cube into $\mathbb{R}^n$

Pages: 213 – 220

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n1.a9

#### Authors

#### Abstract

A di-embedding of the $n$-cube $I^n$ into $\mathbb{R}^n$ is a map $ I^n \to \mathbb{R}^n$ which is a dihomeomorphism onto its image.We show that such a map is, up to a permutation of coordinates, an $n$-fold product of 1-dimensional orientation preserving embeddings $ I^1 \to \mathbb{R}$.

#### Keywords

dihomeomorphism, partially ordered space, progress graph

#### 2010 Mathematics Subject Classification

55Pxx, 68Q85

Published 1 January 2007