Affiliation:
1. Institute of Mathematics Academia Pomeraniensis ul. Arciszewskiego 22d 76–200 Słupsk POLAND
2. Faculty of Mathematics and Computer Science Łódź University ul. Stefana Banacha 22 PL–90 238 Łódź POLAND
Abstract
Abstract
We introduce some family of functions f: ℝ → ℝ modifying Darboux property analogously as it was done in GRANDE, Z.: On a subclass of the family of Darboux functions, Colloq. Math. 117 (2009), 95-104, and changing approximate continuity with 𝓘-approximate continuity, i.e. continuity with respect to the 𝓘-density topology. We prove that our family is a strongly porous set in the space of Darboux functions having the Baire property and that each function from our family is quasi-continuous.
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