A category analogue of the density topology non-homeomorphic with the I-density topology

摘要

The paper deals with the category analogue of a density point and a density topology (with respect to a Lebesgue measure) on the real line which is different from the I-density topology considered in Poreda et al. (Fundam Math 125:167-173, 1985; Comment Math Univ Carol 26:553-563, 1985). This topology called the intensity topology, manifests several properties analogous to that of I-density topology, but there are also differences. The class of function which are continuous as functions from R equipped with an intensity topology to R equipped with the natural topology is included in the first class of Baire Darboux functions.