On some modification of Darboux property
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.