A Note on the Topological Group c0
Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Received: 28 September 2018 / Revised: 22 October 2018 / Accepted: 24 October 2018 / Published: 29 October 2018
A well-known result of Ferri and Galindo asserts that the topological group
is not reflexively representable and the algebra WAP
of weakly almost periodic functions does not separate points and closed subsets. However, it is unknown if the same remains true for a larger important algebra Tame
of tame functions. Respectively, it is an open question if
is representable on a Rosenthal Banach space. In the present work we show that Tame
is small in a sense that the unit sphere S
cannot be separated by a tame function f
. As an application we show that the Gromov’s compactification of
is not a semigroup compactification. We discuss some questions.
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Megrelishvili, M. A Note on the Topological Group c0. Axioms 2018, 7, 77.
Megrelishvili M. A Note on the Topological Group c0. Axioms. 2018; 7(4):77.
Megrelishvili, Michael. 2018. "A Note on the Topological Group c0." Axioms 7, no. 4: 77.
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