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# Def/Domain topograph

Definition of Domain Topograph: The domain topograph is the following combinatorial-geometric object. It consists of the following three sets, and relations of incidence among them.

Let $T = P \cup E \cup F$. Define a relation on $T$, called incidence, as follows:

• If $x,y \in T$, we say that $x$ is incident to $y$ if $x \subset y$ or $y \subset x$.

When discussing lax vectors, bases, and superbases, in the context of the topograph, we use the following terminology:

• We call the elements of $P$ points.
• We call the elements of $E$ edges.
• We call the elements of $F$ faces.
• When $x,y \in T$, and $x$ is incident to $y$, we say that $x$ meets, or touches, $y$.

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Lax superbasis, Def/Lax basis, Def/Lax vector, State/Every lax vector in a lax basis is primitive, State/Every lax basis is contained in exactly two lax superbases, Def/Finite sequence, State/Every primitive lax vector belongs to a lax basis, State/Solutions to homogeneous linear Diophantine equations can be found with the LCM

The following statements and definitions logically rely on the material of this page: Def/Range topograph, and State/The domain topograph has no circuits

To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Binary quadratic forms