Infinite games and quasi-uniform box products

Hope Sabao, Olivier Olela Otafudu

Abstract

We introduce new infinite games, played in a quasi-uniform space, that generalise the proximal game to the framework of quasi-uniform spaces.  We then introduce bi-proximal spaces, a concept that generalises proximal spaces to the quasi-uniform setting. We show that every bi-proximal space is a W-space and as consequence of this, the bi-proximal property is preserved under Σ-products and closed subsets. It is known that the Sorgenfrey line is almost proximal but not proximal. However, in this paper we show that the Sorgenfrey line is bi-proximal, which shows that our concept of bi-proximal spaces is more general than that of proximal spaces. We then present separation properties of certain bi-proximal spaces and apply them to quasi-uniform box products.


Keywords

infinite games; W-spaces; Σ-products; quasi-uniform spaces; quasi-uniform box products

Subject classification

54E15; 54B10; 54E35; 54D15.

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References

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1. Some aspects of quasi-uniform box products
Olivier Olela Otafudu, Hope Sabao
Novi Sad Journal of Mathematics  vol: Accepted  year: 2020  
doi: 10.30755/NSJOM.09860



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt