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On the integral representation of the endomorphisms of Mikuśinski's operator field

We proved in (1) that every continuous endomorphism can be generated on a subring of the field M. More precisely, the ring H of piecewise polynomial functions has the property that every isomorphism from H into M, continuous in the sequential topology of H, can be extended to a continuous endomorphism of M where the notion of continuity in M is the usual sequential one.