  The paper deals with the possibly degenerate behaviour of the exterior
derivative operator defined on $1$-forms on metric measure spaces. The main
examples we consider are the non self-similar Sierpinski carpets recently
introduced by Mackay, Tyson and Wildrick. Although topologically
one-dimensional, they may have positive two-dimensional Lebesgue measure and
carry nontrivial $2$-forms. We prove that in this case the curl operator (and
therefore also the exterior derivative on $1$-forms) is not closable, and that
its adjoint operator has a trivial domain. We also formulate a similar more
abstract result. It states that for spaces that are, in a certain way,
structurally similar to Sierpinski carpets, the exterior derivative operator
taking $1$-forms into $2$-forms cannot be closable if the martingale dimension
is larger than one.
