Infinite games and quasi-uniform box products

Authors

  • Hope Sabao University of Zambia
  • Olivier Olela Otafudu University of the Witwatersrand

DOI:

https://doi.org/10.4995/agt.2019.9679

Keywords:

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

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.

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Author Biographies

Hope Sabao, University of Zambia

Department of Mathematics and Statistics

Olivier Olela Otafudu, University of the Witwatersrand

School of Mathematics

References

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Published

2019-04-01

How to Cite

[1]
H. Sabao and O. Olela Otafudu, “Infinite games and quasi-uniform box products”, Appl. Gen. Topol., vol. 20, no. 1, pp. 57–73, Apr. 2019.

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