The Khalimsky line can be embedded in $\mathbb{R}$ as follows 1:
Let us identify with each even integer $m$ the closed, real interval $[m − 1/2,m + 1/2]$ and with each odd integer $n$ the open interval $]n − 1/2, n + 1/2[$. These intervals form a partition of the Euclidean line $\mathbb{R}$ and we may consider the quotient space.
I am interested in a different embedding, with even integers $n$ to represent $]n÷2 - 1/2, n÷2 + 1/2[$ and odd integers $m$ to represent $m/2$ (i.e. $[m/2, m/2]$).
That definition would align with a uniform cubical complex:
Is there a valid connection between Khalimsky spaces and uniform cubical complexes? I am surprised not to find these two keywords coexisting, except perhaps in the source code of DGtal.
1: Digital Geometry and Khalimsky Spaces, dissertation by Erik Melin
[3]: a software library implementing representation of cubical complex
[4]: interactive webpage depicting the embedding I want, slider should be infinitesimally to the left