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On the comparison of the density type topologies generated by sequences and by functions

100%

Filipczak M. , Filipczak T.

tom Vol. 49, [Z] 2

161-170

In the paper we investigate density type topologies generated by functions f satisfying condition [formula] which are not generated by any sequence.

On the comparison of the density type topologies generated by sequences and by functions

100%

Filipczak M. , Filipczak T.

tom 49

nr 2

In the paper we investigate density type topologies generated by functions \(f\) satisfying condition \(\liminf_{x \gt 0^+} \frac{f(x)}{x}\), which are not generated by any sequence.

Some modifications of density topologies

75%

Horbaczewska G. , Wagner-Bojakowska E.

Journal of Applied Analysis

2001

tom 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.