The width of a resolution proof is the maximal number of literals in any clause of the proof. The space of a proof is the maximal number of memory cells used if the proof is only allowed to resolve on clauses kept in memory. Both of these measures have previously been studied and related to the refutation size of unsatisfiable CNF formulas. Also, the resolution refutation space of a formula has been proven to be at least as large as the refutation width, but it has remained unknown whether space can be separated from width or the two measures coincide asymptotically. We prove that there is a family of k-CNF formulas for which the refutation width in resolution is constant but the refutation space is non-constant, thus solving an open problem mentioned in several previous papers.