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Density topologies on the plane between ordinary and strong

In: Tatra Mountains Mathematical Publications, vol. 44, no. 3
Elżbieta Wagner-Bojakowska - Władysław Wilczyński

Details:

Year, pages: 2009, 139 - 151
Keywords:
density point, density topology, density point with respect to $f$
About article:
Let $C_0$ denote the set of all non-decreasing continuous functions $f\colon (0, 1] \to (0, 1]$ such that $\lim_{x\to 0^+}f(x) =0$ and $f(x) \leq x$ for $x\in (0, 1]$ and let~$A$ be a measurable subset of the plane. We define the notion of a density point of $A$ with respect to $f$\!. This is a starting point to introduce the mapping $D_f$ defined on the family of all measurable subsets of the plane, which is so-called lower density. The mapping $D_f$ leads to the topology $\mathcal T_f$, analogously as for the density topology. The properties of the topologies $\mathcal T_f$ are considered.
How to cite:
ISO 690:
Wagner-Bojakowska, E., Wilczyński, W. 2009. Density topologies on the plane between ordinary and strong. In Tatra Mountains Mathematical Publications, vol. 44, no.3, pp. 139-151. 1210-3195.

APA:
Wagner-Bojakowska, E., Wilczyński, W. (2009). Density topologies on the plane between ordinary and strong. Tatra Mountains Mathematical Publications, 44(3), 139-151. 1210-3195.