Opuscula Math. 34, no. 4 (2014), 799-812
http://dx.doi.org/10.7494/OpMath.2014.34.4.799

Opuscula Mathematica

# On ∞-entropy points in real analysis

Ewa Korczak-Kubiak
Anna Loranty
Ryszard J. Pawlak

Abstract. We will consider $$\infty$$-entropy points in the context of the possibilities of approximation mappings by the functions having $$\infty$$-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.

Keywords: topological entropy, Darboux function, almost continuity, Baire one function, approximately continuous function, pseudo fixed point, topology of uniform convergence, compact-open topology, $$\infty$$-entropy point.

Mathematics Subject Classification: 26A18, 37B40, 26A21, 54H25, 54C08, 54H20.

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• Ewa Korczak-Kubiak
• Łódź University, Faculty of Mathematics and Computer Science, Banacha 22, 90-238 Łódź, Poland
• Anna Loranty
• Łódź University, Faculty of Mathematics and Computer Science, Banacha 22, 90-238 Łódź, Poland
• Ryszard J. Pawlak
• Łódź University, Faculty of Mathematics and Computer Science, Banacha 22, 90-238 Łódź, Poland
• Revised: 2014-02-27.
• Accepted: 2014-02-28.