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A further generalization of the T Ad-density topology

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Języki publikacji
EN
Abstrakty
EN
We present a further generalization of the T Ad-density topology introduced in [Real Anal. Exchange 32 (2006/07), 349–358] as a generalization of the density topology. We construct an ascending sequence [wzór] of density topologies which leads to the [wzór]-density topology including all previous topologies. We examine several basic properties of the topologies.
Wydawca
Rocznik
Strony
283--304
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
  • Institute of Mathematics, Łódź University of Technology, Wólczańska 215, 90-924 Łódź, Poland
Bibliografia
  • [1] V. Aversa and W. Wilczyński, Simple density topology, Rend. Circ. Mat. Palermo (2) 53 (2004), no. 3, 344-352.
  • [2] K. Ciesielski, L. Larson and K. Ostaszewski, I-density continuous functions, Mem. Amen Math. Soc. 515 (1994).
  • [3] A. Denjoy, Memoire sur les derives des fonctions continues, J. Math. Pures Appl. 1 (1915), 105-240.
  • [4] M. Filipczak and T. Filipczak, On f-density topologies, Topology Appl. 155 (2008), 1980-1989.
  • [5] C. Goffman, C. J. Neugebauer and T. Nishiura, Density topology and approximate continuity, Duke Math. J. 28 (1961), 497-505.
  • [6] C. Goffman and D. Waterman, Approximately continuous transformations, Proc. Amen Math. Soc. 12 (1961), 116-121.
  • [7] O. Haupt and H. Pauc, La topologie de Denjoy envisagee comme vraie topologie, C. R. Acad. Sci. Paris 234 (1952), 390-392.
  • [8] J. C. Oxtoby, Measure and Category, Graduate Texts in Math. 2, Springer, Berlin, 1980.
  • [9] W. Poreda, E. Wagner-Bojakowska and W. Wilczyński, A category analogue of the density topology, Fund. Math. 125 (1985), 167-173.
  • [10] W. Poreda, E. Wagner-Bojakowska and W. Wilczyński, Remarks on I-density and I-approximately continuous functions, Comm. Math. Univ. Carolinae 26 (1985), no. 3, 553-563.
  • [11] D. A. Rose, D. Jankowic and T. R. Hamlett, Lower density topologies, in: Papers on General Topology and Applications, Ann. N. Y. Acad. Sci. 704, The New York Academy of Sciences, New York (1993), 309-321.
  • [12] F. D. Tali, The density topology, Pacific J. Math. 62 (1976), no. 1, 275-284.
  • [13] W. Wilczyński, A generalization of the density topology, Real. Anal. Exchange 8 (1982/83), no. 1, 16-20.
  • [14] W. Wilczyński, Density topologies, in: Handbook of Measure Theory, Elsevier, Amsterdam (2002), 675-702.
  • [15] W. Wilczyński and W. Wojdowski, Complete density topology, Indag. Math. 18 (2007), no. 2, 295-303.
  • [16] W. Wojdowski, A generalization of the density topology, Real Anal. Exchange 32 (2006/07), no. 2, 349-358.
  • [17] W. Wojdowski, On a generalization of the density topology on the real line, Real Anal. Exchange 33 (2007/08), no. 1, 199-214.
  • [18] W. Wojdowski, Corrigendum in: A generalization of density topology and On generalization of the density topology on the real line, Real Anal. Exchange 37 (2011/12), no. 2, 519-522.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-46bac18e-8ec2-4e54-9368-84f0fcadc122
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