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Comparison of ψ -sparse topologies

Goździewicz-Smejda A., Łazarow E.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2009

Vol. 14

21-36

The paper includes a necessary condition and sufficient conditions under which two ψ -sparse topologies generated by two functions ψ1 and ψ 2 are equal. Additionally we proved that the intersection of all ψ -sparse topologies is equal to the Hashimoto topology.

Some modifications of density topologies

Horbaczewska G., Wagner-Bojakowska E.

Journal of Applied Analysis

2001

Vol. 7, nr 1

91-105

In this paper we introduce two topologies on the plane connected with the notions of density and I-density. Their definitions are based on the notion of a regular density point. We investigate connections between them and the density and I-density topologies on the plane and on the real line. We consider axioms of separation and functions continuous with respect to these topologies.