Convergence semigroup categories

• Richardson, Gary ^[1] ; Boustique, H. ^[1] ; Mikusinski, Piotr ^[1]
  1. [1] University of Central Florida

     University of Central Florida

     Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 11, Nº. 2, 2010, págs. 67-88
• Idioma: inglés
• DOI: 10.4995/agt.2010.1709
• Enlaces
  • Texto completo
• Resumen

  • Properties of the category consisting of all objects of the form (X, S, λ) are investigated, where X is a convergence space, S is a commutative semigroup, and λ: X × S → X is a continuous action. A “generalized quotient” of each object is defined without making the usual assumption that for each fixed g ∈ S, λ(., g) : X  → X is an injection.

• Referencias bibliográficas
  • J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley Pub., 1990.
  • R. Beattie and H.-P. Butzmann, Convergence Structures and Applications to Functional Analysis, Kluwer Acad. Pub., Dordrecht, 2002. http://dx.doi.org/10.1007/978-94-015-9942-9
  • H. Boustique, P. Mikusinski and G. Richardson, Convergence semigroup actions: Generalized quotients, Appl. Gen. Topol. 10 (2009), 173–186.
  • D. Bradshaw, M. Khosravi, H. M. Martin and P. Mikusinski, On categorical and topological properties of generalized quotients (seminar notes),...
  • J. Burzyk, C. Ferens and P. Mikusinski, On the topology of generalized quotients, Appl. Gen. Topol. 9 (2008), 205–212.
  • A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Volume 1, Amer. Math. Soc., Providence, R.I, 1961.
  • D. Kent, Convergence quotient maps, Fund. Math. 65 (1969), 197–205.
  • D. Kent and G. Richardson, The regularity series of a convergence space, Bull. Aust. Math. Soc. 13 (1975), 21–44. http://dx.doi.org/10.1017/S0004972700024229
  • D. C. Kent and G. D. Richardson, The regularity series of a convergence space II, Bull. Aust. Math. Soc. 15 (1976), 223–243. http://dx.doi.org/10.1017/S0004972700022590
  • M. Khosravi, Pseudoquotients: Construction, applications, and their Fourier transform, Ph.D. dissertation, Univ. of Central Florida, Orlando,...
  • P. Mikusinski, Boehmians and generalized functions, Acta Math. Hungar. 51 (1988), 271–281. http://dx.doi.org/10.1007/BF01903334
  • P. Mikusinski, Generalized quotients with applications in analysis, Methods and Applications of Anal. 10(2003), 377–386. http://dx.doi.org/10.4310/MAA.2003.v10.n3.a4
  • W. Park, Convergence structures on homeomorphism groups, Math. Ann. 199(1972), 45–54. http://dx.doi.org/10.1007/BF01419575
  • W. Park, A note on the homeomorphism group of the rational numbers, Proc. Amer. Math. Soc. 42(1974), 625–626. http://dx.doi.org/10.1090/S0002-9939-1974-0341368-9
  • G. Preuss, Foundations of Topology: An Approach to Convenient Topology, Kluwer Acad. Pub., Dordrecht, 2002. http://dx.doi.org/10.1007/978-94-010-0489-3
  • N. Rath, Action of convergence groups, Topology Proc. 27 (2003), 601–612.
  • G. D. Richardson, A Stone-Cech compactification for limit spaces, Proc. Amer. Math. Soc. 25 (1970), 403–404.
  • G. D. Richardson and D. C. Kent, Regular compactifications of convergence spaces, Proc. Amer. Math. Soc. 31 (1972), 571–573. http://dx.doi.org/10.1090/S0002-9939-1972-0286074-2