A pseudocompact Tychonoff space all countable subsets of which are closed and C1-embedded

Let X be a Tychonoff space and let all subsets of cardinality ⩽τ of X be closed (and C¹-embedded). Then X can be embedded as a closed subspace in a pseudocompact Tychonoff space Y such that all subsets of cardinality ⩽τ of Y are closed (and C¹-embedded). As an application of this result we construct a pseudocompact connected left-separated Tychonoff space having all its subsets of cardinality ⩽τ closed and C¹-embedded.