Metrizability of topological polygroups

Subject Areas : Statistics

Mehrdad Kahrazeh ¹ , Javad Jamalzadeh ²

1 - Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2 - Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Received: 2020-05-18 Accepted : 2022-11-30 Published : 2022-08-23

Keywords: پلی‌گروه توپولوژیکی, پیش‌نرم, متریک‌پذیری,

Abstract :

One of the most important parts of topological structures is metrizability, which creates the conditions for a metric such as d to be found so that the topology obtained from this metric is the same as the original topology. Topological algebraic structures that are closely related to ℝ and its resulting spaces. For example, in topological groups, as a topological algebraic structure, there are very close properties with metric and soft spaces, such as being completely regular, being Hausdorff,…. .In terms of metrizability, there is an astonishing case called the Birkhoff - Kakutani case, which states that a topological group is metricable if and only if it is the first-countable. In this manuscript, we make topological polygroup metrizable. We do this by definition of the prenorm on topological polygoups, and finally we prove the fundamental theorem of metrizability on topological polygroups Like topological groups, it is the first-countable of topological polygroup.

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