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Barrera, de la, Daniel
(2014)
*Q is not a Mackey group.*
Topology and its applications
(178).
pp. 265-275.
ISSN 0166-8641

PDF
Restringido a Repository staff only 382kB |

Official URL: http://www.sciencedirect.com/science/article/pii/S0166864114003927#

## Abstract

The aim of this paper is to prove that the usual topology in Q inherited from the real line is not a Mackey topology in the sense defined in [5]. To that end, we find a locally quasi-convex topology on Q/Z, the torsion group of T, which is strictly finer than the one induced by the euclidean topology of T. Nevertheless, both topologies on Q/Z admit the same character group. Since the property of being a Mackey group is preserved by LQC quotients, we obtain that the usual topology in Q is not the finest compatible topology. In other words, there is a strictly finer locally quasi-convex topology on Q giving rise to the same dual group as Q with the usual topology. A wide class of countable subgroups of the torus T, which are not Mackey are also obtained ( Remark 3.7). Obviously, they are precompact, metrizable and locally quasi-convex groups.

Item Type: | Article |
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Uncontrolled Keywords: | Locally quasi-convex; Mackey topology; Dual group |

Subjects: | Sciences > Mathematics |

ID Code: | 29001 |

Deposited On: | 04 Mar 2015 11:33 |

Last Modified: | 12 Dec 2018 15:12 |

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