On f-density topologies

摘要

In the paper there are discussed separation axioms for different f-density topologies on the real line. It is proved that f-density topologies generated by functions f with liminf_(x → 0)+ f(x)/x > 0 are completely regular but f-density topologies generated by f such that liminf_(x → 0)+ f(x)/x = 0 are not regular.