About porosity of some Świątkowski functions in the space of quasi-continuous functions

Abstract

In the paper by M. Filipczak, G. Ivanova and J. Wódka, Comparison of some families of real functions in porosity terms, Math. Slovaca 67(5) (2017), 11551164, it was proved that the family of quasi-continuous Świątkowski functions is porous but not strongly porous in the space of quasi-continuous functions. We improved this result. We found the unique number q = 2=3 such that the family of quasi-continuous Świątkowski functions is lower q-porous in this space.

Key words: Darboux property, strong Świątkowski property, Baire property, quasi-continuity, porosity.