Infinite games and quasi-uniform box products

• Autores: Hope Sabao, Olivier Olela Otafudu
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 20, Nº. 1, 2019, págs. 57-73
• Idioma: inglés
• DOI: 10.4995/agt.2019.9679
• Enlaces
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• Resumen

  • 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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