On the topology of generalized quotients

• Burzyk, Józef ^[2] ; Ferens, Cezary ; Mikusinski, Piotr ^[1]
  1. [1] University of Central Florida

     University of Central Florida

     Estados Unidos

     
  2. [2] Technical University of Silesia
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 9, Nº. 2, 2008, págs. 205-212
• Idioma: inglés
• DOI: 10.4995/agt.2008.1801
• Enlaces
  • Texto completo
• Resumen

  • Generalized quotients are defined as equivalence classes of pairs (x, f), where x is an element of a nonempty set X and f is an element of a commutative semigroup G acting on X. Topologies on X and G induce a natural topology on B(X,G), the space of generalized quotients. Separation properties of this topology are investigated.

• Referencias bibliográficas
  • D. Bradshaw, M. Khosravi, H. M. Martin and P. Mikusinski, On Categorical and Topological Properties of Generalized Quotients, preprint.
  • J. Burzyk and P. Mikusinski, A generalization of the construction of a field of quotients with applications in analysis, Int. J. Math. Sci....
  • J. H. Carruth, J. A. Hildebrant, and R. J. Koch, The Theory of Topological Semigroups (Marcel Dekker, New York, 1983).
  • P. Mikusinski, Generalized Quotients with Applications in Analysis, Methods Appl. Anal. 10 (2004), 377–386.