Density and \(\mathcal I\)-density continuous homeomorphisms
The aim of the paper is to prove that the following classes of real functions of a real variable are closed with respect to addition: density continuous increasing homeomorphisms, \(\mathcal I\)-density continuous increasing homeomorphisms, increasing homeomorphisms preserving \(\mathcal I\)- density points. A similar fact concerning increasing homeomorphisms preserving density points has been proved by J. Niewiarowski in 1980. The theorems are not longer true if one of the homeomorphisms is decreasing even when their sum is still increasing.
\(\mathcal I\)-density continuous increasing homeomorphisms
scientific article; zbMATH DE number 465096