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LOCALLY COMPACT TOPOLOGICAL GROUPS ANDCOFINAL COMPLETENESS

Published online by Cambridge University Press:  08 January 2001

SALVADOR ROMAGUERA  and
MANUEL SANCHIS
SALVADOR ROMAGUERA
Affiliation:
Departamento de Matemática Aplicada, Escuela de Caminos, Universidad Politécnica de Valencia, 46071 Valencia, Spain; [email protected]
MANUEL SANCHIS
Affiliation:
Departamento de Matemáticas, Universidad Jaume I, Campus del Riu Sec, 12071 Castellón, Spain; [email protected]
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Abstract

It is proved that a Tychonoff topological group is locally compact if and only if it is of pointwise countable type and its left uniformity is cofinally complete. From this result a characterization is derived of those T0 paratopological groups (X, τ) of pointwise countable type for which (X, τ ∨ τ−1) is locally compact and also a characterization is deduced of locally pseudocompact topological groups in terms of cofinal completeness. Also characterized are the Tychonoff topological groups of pointwise countable type for which their left uniformity has property U. Finally, cofinal completeness of the Hausdorff–Bourbaki uniformity of a topological group is studied.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 451 - 460
Copyright
The London Mathematical Society 2000

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