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On group uniformities on square of a space and extending pseudometrics II

Published online by Cambridge University Press:  17 April 2009

Michael G. Tkačenko
Michael G. Tkačenko
Affiliation:
Departamento de MatemáticasUniversidad Autónoma MetropolitanaAv. Michoacan y La PurísimaIztapalapa, A.P. 55–532, C.P. 09340México, D.F. e-mail: mich@xanum.uam.mx
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Abstract

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We find topological conditions on a space X under which the left (right, or two-sided) uniformity of the free topological group F(X) induces the universal uniformity or the product uniformity ux × ux on the square of X. Special attention is given to kω metrisable spaces. The main technical tool in the paper is an extension of certain continuous pseudometrics from X2 to F(X) considered by the author in the previous volume of this journal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 1 , August 1995 , pp. 41 - 61
Copyright
Copyright © Australian Mathematical Society 1995

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