Extensions of topological algebras
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We prove that, in the class of commutative topological algebras with separately continuous multiplication, an element is permanently singular if and only if it is a topological divisor of zero. This extends the result given by R. Arens [1] for the Banach algebra case. We also give sufficient conditions for non-removability of ideals in commutative topological algebras with jointly continuous multiplication.
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Fernández Carrión, Antonio et al. «Extensions of topological algebras». Collectanea Mathematica, vol.VOL 40, n.º 1, pp. 55-66, https://raco.cat/index.php/CollectaneaMathematica/article/view/56860.
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