PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2011 | 9 | 5 | 1057-1066
Tytuł artykułu

A category Ψ-density topology

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Ψ-density point of a Lebesgue measurable set was introduced by Taylor in [Taylor S.J., On strengthening the Lebesgue Density Theorem, Fund. Math., 1958, 46, 305–315] and [Taylor S.J., An alternative form of Egoroff’s theorem, Fund. Math., 1960, 48, 169–174] as an answer to a problem posed by Ulam. We present a category analogue of the notion and of the Ψ-density topology. We define a category analogue of the Ψ-density point of the set A at a point x as the Ψ-density point at x of the regular open representation of A.
Słowa kluczowe
Twórcy
Bibliografia
  • [1] Ciesielski K., Larson L, Ostaszewski K., J-Density Continuous Functions, Mem. Amer. Math. Soc, 515, American Mathematical Society, Providence, 1994
  • [2] Erdös P., Some remarks on set theory, Ann. of Math., 1943, 44(4), 643–646 http://dx.doi.org/10.2307/1969101
  • [3] Goffman C, Neugebauer C.J., Nishiura T., Density topology and approximate continuity, Duke Math. J., 1961, 28(4), 497–505 http://dx.doi.org/10.1215/S0012-7094-61-02847-2
  • [4] Goffman C, Waterman D., Approximately continuous transformations, Proc. Amer. Math. Soc, 1961, 12(1), 116–121 http://dx.doi.org/10.1090/S0002-9939-1961-0120327-6
  • [5] Haupt O., Pauc Ch., La topologie approximative de Denjoy envisagée comme vraie topologie, C. R. Acad. Sci. Paris, 1952, 234, 390–392
  • [6] Hejduk J., On the abstract density topologies, preprint available at http://www.math.uni.lodz.pl/preprints,483.html
  • [7] Kuratowski C., Ulam S., Quelques propriétés topologiques du produit combinatoire, Fund. Math., 1932, 19, 247–251
  • [8] Lukěs J., Malý J., Zajíčcek L., Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math., 1189, Springer, Berlin, 1986
  • [9] Miller H.I., Baire outer kernels of sets, Publ. Inst. Math. (Beograd) (N.S.), 1981, 30(44), 117–122
  • [10] O’Malley R.J., Approximately differentiable functions: the r topology, Pacific J. Math., 1977, 72(1), 207–222
  • [11] Ostaszewski K., Continuity in the density topology, Real Anal. Exchange, 1982, 7(2), 259–270
  • [12] Oxtoby J.C., Measure and Category, 2nd ed., Grad. Texts in Math., 2, Springer, New York-Berlin, 1980
  • [13] Poreda W., Wagner-Bojakowska E., Wilczyński W., A category analogue of the density topology, Fund. Math., 1985, 125(2), 167–173
  • [14] Poreda W., Wagner-Bojakowska E., Wilczyński W., Remarks on I-density and I-approximately continuous functions, Comment. Math. Univ. Carolin., 1985, 26(3), 553–563
  • [15] Sierpiński W., Sur la dualité entre la première catégorie et la mesure nulle, Fund. Math., 1934, 22, 276–280
  • [16] Sierpiński W., Hypothèse du Continu, Monogr. Mat., 4, Warszawa-Lwów, 1934
  • [17] Sierpiński W., Lusin N., Sur une décomposition dun intervalle en une infinité non dénombrable densembles non measurables, C. R. Acad. Sci. Paris, 1917, 165, 422–424
  • [18] Szpilrajn E., Remarques sur les fonctions complètement additives densemble et sur les ensembles jouissant de la propriètè de Baire, Fund. Math., 1934, 22, 303–311
  • [19] Tall F.D., The density topology, Pacific J. Math., 1976, 62(1), 275–284
  • [20] Taylor S.J., On strengthening the Lebesgue Density Theorem, Fund. Math., 1958, 46, 305–315
  • [21] Taylor S.J., An alternative form of Egoroffs theorem, Fund. Math., 1960, 48, 169–174
  • [22] Terepeta M., Wagner-Bojakowska E., ψ-density topology, Rend. Circ. Mat. Palermo, 1999, 48(3), 451–476 http://dx.doi.org/10.1007/BF02844336
  • [23] Wagner-Bojakowska E., Remarks on ψ-density topology, Atti Sem. Mat. Fis. Univ. Modena, 2001, 49(1), 79–87
  • [24] Wagner-Bojakowska E., Wilczyński W., The interior operation in a ψ-density topology, Rend. Circ. Mat. Palermo, 2000, 49(1), 5–26 http://dx.doi.org/10.1007/BF02904217
  • [25] Wagner-Bojakowska E., Wilczyński W., Comparison of ψ-density topologies, Real. Anal. Exchange, 2000, 25(2), 661–672
  • [26] Wilczyński W., A generalization of the density topology, Real. Anal. Exchange, 1983, 8(1), 16–20
  • [27] Wilczyński W., Density topologies, In: Handbook of Measure Theory, North-Holland, Amsterdam, 2002, 675–702 http://dx.doi.org/10.1016/B978-044450263-6/50016-6
  • [28] Wojdowski W., Density topologies involving measure and category, Demonstratio Math., 1989, 22(3), 797–812
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0069-0
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.