The metrizability of L-topological groups

• Main Authors: Fatma Bayoumi, Ismail Ibedou
• Format: Article
• Language: English
• Published: SpringerOpen 2013-10-01
• Series: Journal of the Egyptian Mathematical Society
• Subjects: Countable L-filters; Countable L-topological spaces; L-topological groups; Separated L-topological groups; L-metric spaces; L-pseudo-metric spaces
• Online Access: http://www.sciencedirect.com/science/article/pii/S1110256X13000424
• ISSN: 1110-256X

In this study, we study the metrizability of the notion of L-topological group defined by Ahsanullah 1988. We show that for any (separated) L-topological group there is an L-pseudo-metric (L-metric), in sense of Gähler which is defined using his notion of L-real numbers, compatible with the L-topology of this (separated) L-topological group. That is, any (separated) L-topological group is pseudo-metrizable (metrizable).