Selections generating new topologies

• Autores: Valentin Gutev, Artur Hideyuki Tomita
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 51, Nº 1, 2007, págs. 3-15
• Idioma: inglés
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• Resumen

  • Every (continuous) selection for the non-empty 2-point subsets of a space $X$ naturally defines an interval-like topology on $X$. In the present paper, we demonstrate that, for a second-countable zero-dimensional space $X$, this topology may fail to be first-countable at some (or, even any) point of $X$. This settles some problems stated in [7].