Function Spaces and Strong Variants of Continuity

• Kohli, J.K. ^[1] ; Singh, D. ^[1]
  1. [1] University of Delhi

     University of Delhi

     India

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 9, Nº. 1, 2008, págs. 33-38
• Idioma: inglés
• DOI: 10.4995/agt.2008.1867
• Enlaces
  • Texto completo
• Resumen

  • It is shown that if domain is a sum connected space and range is a T0-space, then the notions of strong continuity, perfect continuity and cl-supercontinuity coincide. Further, it is proved that if X is a sum connected space and Y is Hausdorff, then the set of all strongly continuous (perfectly continuous, cl-supercontinuous) functions is closed in Y X in the topology of pointwise convergence. The results obtained in the process strengthen and extend certain results of Levine and Naimpally.

• Referencias bibliográficas
  • R. F. Brown, Ten topologies for X×Y , Quarterly J. Math. (Oxford) 14 (1963), 303–319. http://dx.doi.org/10.1093/qmath/14.1.303
  • S. P. Franklin, Natural covers, Composito Mathematica 21 (1969), 253–261.
  • J. L. Kelly, General Topology, D. Van Nostand Company, Inc., 1955.
  • J. K. Kohli, A class of spaces containing all connected and all locally connected spaces, Math. Nachricten 82 (1978), 121–129. http://dx.doi.org/10.1002/mana.19780820113
  • N. Levine, Strong continuity in topological spaces, Amer. Math. Monthly 67 (1960), 269. http://dx.doi.org/10.2307/2309695
  • E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 7 (1951), 152–182. http://dx.doi.org/10.1090/S0002-9947-1951-0042109-4
  • S. A. Naimpally, On strongly continuous functions, Amer. Math. Monthly 74 (1967), 166–168. http://dx.doi.org/10.2307/2315609
  • T. Noiri, Supercontinuity and some strong forms of continuity, Indian J. Pure. Appl. Math. 15, no. 3 (1984), 241–250.
  • I. L. Reilly and M. K. Vamanamurthy, On super-continuous mappings, Indian J. Pure. Appl. Math. 14, no. 6 (1983), 767–772.
  • D. Singh, cl-supercontinuous functions, Applied Gen. Top. (accepted).
  • R. Staum, The Algebra of bounded continuous functions into a nonarchimedean field, Pac. J. Math. 50, no. 1 (1974), 169–185. http://dx.doi.org/10.2140/pjm.1974.50.169
  • L. A. Steen and J. A. Seeback, Jr., Counter Examples in Topology, Springer Verlag, New York, 1978. http://dx.doi.org/10.1007/978-1-4612-6290-9