  Let $\mathbb T$ be the differential field of transseries. We establish some
basic properties of the dimension of a definable subset of ${\mathbb T}^n$,
also in relation to its codimension in the ambient space ${\mathbb T}^n$. The
case of dimension $0$ is of special interest, and can be characterized both in
topological terms (discreteness) and in terms of the
Herwig-Hrushovski-Macpherson notion of co-analyzability. The proofs use results
by the authors from "Asymptotic Differential Algebra and Model Theory of
Transseries", the axiomatic framework for "dimension" in [L. van den Dries,
"Dimension of definable sets, algebraic boundedness and Henselian fields", Ann.
Pure Appl. Logic 45 (1989), no. 2, 189-209], and facts about co-analyzability
from [B. Herwig, E. Hrushovski, D. Macpherson, "Interpretable groups, stably
embedded sets, and Vaughtian pairs", J. London Math. Soc. (2003) 68, no. 1,
1-11].
