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arXiv · 2002.06365

On discontinuity of derivations, inducing non-unique complete metric topologies

S. R. Patel
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Abstract

We give a simple method for constructing commutative Frechet algebras which admit two inequivalent Frechet algebra topologies. The result is applied to show that the action of any non-algebraic analytic function may fail to be uniquely defined among other useful applications. We give an affirmative answer to a question of Loy from 1974. We also obtain the uniqueness of the Frechet algebra topology of certain Frechet algebras with finite dimensional radicals.

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S. R. Patel. 2020-02-15. On discontinuity of derivations, inducing non-unique complete metric topologies. https://arxiv.org/abs/2002.06365

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