  We introduce the notion of spaces with weak relative cohomology and show the
acyclicity of the complement $Q\setminus X$ in the Hilbert cube $Q$ of a
compactum $X$ with weak relative cohomology. As a corollary we obtain the
acyclicity of the complement results when
  (a) $X$ is weakly infinite dimensional;
  (b) $X$ has finite cohomological dimension.
