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A Tychonoff space which contains no realcompact space as a dense subspace is constructed. Let      D R \mathcal {D}\mathcal {R}       be the class of all spaces which contain some realcompact spaces as dense subspaces. Then, as a consequence of the above result, it follows that      D R \mathcal {D}\mathcal {R}       is not closed-hereditary.

A space which contains no realcompact dense subspace