Product metrics and boundedness

• Beer, Gerald ^[1]
  1. [1] California State University Los Angeles

     California State University Los Angeles

     Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 9, Nº. 1, 2008, págs. 133-142
• Idioma: inglés
• DOI: 10.4995/agt.2008.1873
• Enlaces
  • Texto completo
• Resumen

  • This paper looks at some possible ways of equipping a countable product of unbounded metric spaces with a metric that acknowledges the boundedness characteristics of the factors.

• Referencias bibliográficas
  • G. Beer, On metric boundedness structures, Set-Valued Anal. 7 (1999), 195-208. http://dx.doi.org/10.1023/A:1008720619545
  • G. Beer, On convergence to infinity, Monat. Math. 129 (2000), 267-280. http://dx.doi.org/10.1007/s006050050075
  • G. Beer, Metric bornologies and Kuratowski-Painlev´e convergence to the empty set, J. Convex Anal. 8 (2001), 279-289.
  • J. Borwein, M. Fabian, and J. Vanderwerff, Locally Lipsschitz functions and bornological derivatives, CECM Report no. 93:012.
  • A. Caterino and S. Guazzone, Extensions of unbounded topological spaces, Rend. Sem. Mat. Univ. Padova 100 (1998), 123-135.
  • A. Caterino, T. Panduri, and M. Vipera, Boundedness, one-pont extensions, and B-extensions, Math. Slovaca 58, no. 1 (2008), 101–114. http://dx.doi.org/10.2478/s12175-007-0058-8
  • J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.
  • R. Engelking, General topology, Polish Scientific Publishers, Warsaw, 1977.
  • H. Hogbe-Nlend, Bornologies and functional analysis, North-Holland, Amsterdam, 1977.
  • S.-T. Hu, Boundedness in a topological space, J. Math Pures Appl. 228 (1949), 287-320.
  • S.-T. Hu, Introduction to general topology, Holden-Day, San Francisco, 1966.
  • A. Lechicki, S. Levi, and A. Spakowski, Bornological convergences, J. Math. Anal. Appl. 297 (2004), 751-770. http://dx.doi.org/10.1016/j.jmaa.2004.04.046
  • A. Taylor and D. Lay, Introduction to functional analysis, Wiley, New York, 1980.
  • H. Vaughan, On locally compact metrizable spaces, Bull. Amer. Math. Soc. 43 (1937),532-535. http://dx.doi.org/10.1090/S0002-9904-1937-06593-1