On \( \mathcal{S} \)-approximately continuous functions

Abstract

This paper concerns a generalization of approximately continuous functions, namely \( \mathcal{S} \)-approximately continuous functions. This notion is associated with \( \mathcal{S} \)-density points, where \( \mathcal{S} \) is a sequence of measurable sets tending to 0. Moreover, we present some properties of these functions and show their connection with measurable functions, functions from the first Baire class, and Darboux functions.

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Correspondence to Renata Wiertelak.

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Wiertelak, R. On \( \mathcal{S} \)-approximately continuous functions. Lith Math J (2020). https://doi.org/10.1007/s10986-020-09502-9

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Keywords

  • approximately continuous functions
  • density topology
  • approximately continuous functions
  • Baire one functions
  • Darboux functions

MSC

  • 26A15
  • 54A10
  • 26A21