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We will consider ∞-entropy points in the context of the possibilities of approximation mappings by the functions having ∞-entropy points and belonging to essential (from the point of view of real analysis theory) classes of functions: almost continuous, Darboux Baire one and approximately continuous functions.
Czasopismo
Rocznik
Tom
Strony
799--812
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
- Łódz University Faculty of Mathematics and Computer Science Banacha 22, 90-238 Łódz, Poland
autor
- Łódz University Faculty of Mathematics and Computer Science Banacha 22, 90-238 Łódz, Poland
autor
- Łódz University Faculty of Mathematics and Computer Science Banacha 22, 90-238 Łódz, Poland
Bibliografia
- [1] R.L. Adler, A.G. Konheim, M.H. McAndrew, Topological Entropy, Trans. Amer. Math. Soc. 114 (1965), 309–319.
- [2] L. Alsedà, J. Llibre, M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, World Scientific, 1993.
- [3] L.S. Block, W.A. Coppel, Dynamics in one dimension, Lecture Notes in Mathematics 1513, Springer-Verlag, Berlin, 1992.
- [4] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401–414; erratum, 181 (1973), 509–510.
- [5] J.B. Brown, Almost continuity of the Cesàro-Vietoris function, Proc. Amer. Math. Soc. 49 (1975) 1, 185–188.
- [6] A.M. Bruckner, Differentiation of Real Functions, CRM Monogr. Ser., vol. 5, AMS, Providence, RI, 1994.
- [7] A.M. Bruckner, J.G. Ceder, Darboux continuity, Jbr. Deutsch Math. Verein 67 (1965), 93–117.
- [8] A. Crannell, M. Frantz, M. LeMasurier, Closed relations and equivalence classes of quasicontinuous functions, Real Anal. Exchange 31 (2005/06) 2, 409–423.
- [9] M. Ciklová, Dynamical systems generated by functions with connected G graphs, Real Anal. Exchange, 30 (2004/2005) 2, 617–638.
- [10] A. Denjoy, Sur les fonctions dérivées sommables, Bull. Soc. Math. France 43 (1916), 161–248.
- [11] E.I. Dinaburg, A connection between various entropy characterizations of dynamical systems, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 324–366.
- [12] H.B. Hoyle III, Connectivity maps and almost continuous functions, Duke Math. J. 37 (1970) 4, 671–680.
- [13] J.M. Jastrzebski, J.M. Jedrzejewski, T. Natkaniec, On some subclass of Darboux functions, Fund. Math. 138 (1991) 3, 165–173.
- [14] J.C. Kelly, Bitopological spaces, Proc. London Math. Soc. 13 (1963) 3, 71–89.
- [15] J.S. Lipinski, On Darboux points, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978) 11, 689–873.
- [16] A. Maliszewski, The maximal class with respect to maximums for the family of almost continuous functions, Real Anal. Exchange 32 (2006/07), 313–318.
- [17] W. de Melo, S. van Strien, One-Dimensional Dynamics, Springer-Verlag, Berlin Heidelberg, 1993.
- [18] S.A. Naimpally, Graph topology for function spaces, Trans. Amer. Math. Soc. 123 (1966), 267–272.
- [19] T. Natkaniec, Almost continuity, Real Anal. Exchange 17 (1991/92), 462–520.
- [20] T. Natkaniec, Almost continuity, Habilitation Thesis, 1992.
- [21] T. Natkaniec, P. Szuca, On Pawlak’s problem concerning entropy of almost continuous function, Colloq. Math. 121 (2010) 1, 107–111.
- [22] R.J. Pawlak, On the entropy of Darboux functions, Colloq. Math. 116 (2009) 2, 227–241.
- [23] R.J. Pawlak, A. Loranty, A. Bakowska, On the topological entropy of continuous and almost continuous functions, Topology Appl. 158 (2011), 2022–2033.
- [24] B.D. Smith, An alternate characterization of continuity, Proc. Amer. Math. Soc. 39 (1973) 2, 318–320.
- [25] J. Stallings, Fixed point theorem for connectivity maps, Fund. Math. 47 (1959) 3, 249–263.
- [26] P. Szuca, Punkty stałe odwzorowan typu Darboux, Ph.D. Thesis, Gdansk, 2003 [in Polish].
- [27] P. Szuca, Sharkovski˘ı’s theorem holds for some discontinuous functions, Fund. Math.
- 179 (2003), 27–41.
- [28] W. Wilczynski, Density topologies, Chapter 15 in Handbook of Measure Theory, E. Pap (ed.), Elsevier, 2002, 675–702.
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Bibliografia
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bwmeta1.element.baztech-7a2fdede-7220-4f66-aafc-fb8699bce862