Asymptotic structures of cardinals

• Petrenko, Oleksandr ^[1] ; Protasov, Igor V. ^[2] ; Slobodianiuk, Sergii ^[1]
  1. [1] Kyiv National University
  2. [2] Kyiv University
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 15, Nº. 2, 2014, págs. 137-146
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • A ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F)  can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define F using a natural order structure on k. We characterize balleans up to coarse equivalence, give the criterions of metrizability and cellularity, calculate the basic cardinal invariant of these balleans. We conclude the paper with discussion of some special ultrafilters on cardinal balleans.