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We explicitly compute the Dolbeault cohomologies of certain domains incomplex space generalizing the classical Hartogs figure. The cohomology groupsare non-Hausdorff topological vector spaces, and it is possible to identify thereduced (Hausdorff) and the indiscrete part of the cohomology.

Some non-pseudoconvex domains with explicitly computable non-Hausdorff Dolbeault cohomology