My question is very simple, but I wasn't able to find an answer in various sources. Cell-complexes are commonly presented using an inductive construction where $n$-cells are attached to $(n-1)$-cells, starting with the data of a collection $X^0$ of $0$-cells.
But sometimes, one will define a $2$-cell for instance, as being a sub-cell complex of something, raising the question: can a cell complex $0$-skeleton be empty? And more generally, can a cell-complex have empty skeletons until a dimension $k$?
It doesn't seem absurd to me that the answer should be yes, but it worries me to never see the case taken into account in the inductive construction.