Facebook Instagram Twitter RSS Feed PodBean Back to top on side

Density topologies on the plane between ordinary and strong. II

In: Tatra Mountains Mathematical Publications, vol. 62, no. 1
Elżbieta Wagner-Bojakowska - Władysław Wilczyński
Detaily:
Rok, strany: 2015, 13 - 25
Kľúčové slová:
density point, density topology, density point with respect to $f$
O článku:
Let $C_0$ denote a set of all non-decreasing continuous functions $f : (0, 1] \to (0, 1]$ such that $\lim_{x\to 0^+}f(x) =0$ and $f(x) ≤ x$ for every $x\in (0, 1]$, and let $A$ be a measurable subset of the plane. The notions of a density point of $A$ with respect to $f$ and the mapping $D_f$ defined on the family of all measurable subsets of the plane were introduced in Wagner-Bojakowska, E.—Wilczyński, W.: \textit{Density topologies on the plane between ordinary and strong,} Tatra Mt. Math. Publ. \textbf{44} (2009), 139--151. This mapping is a lower density, so it allowed us to introduce the topology $\mathcal T_f$, analogously to the density topology. In this note, properties of the topology $\mathcal T_f$ and functions approximately continuous with respect to $f$ are considered. We prove that $(\Bbb R^2\!, \mathcal T_f)$ is a completely regular topological space and we study conditions under which topologies generated by two functions $f$ and $g$ are equal.
Ako citovať:
ISO 690:
Wagner-Bojakowska, E., Wilczyński, W. 2015. Density topologies on the plane between ordinary and strong. II. In Tatra Mountains Mathematical Publications, vol. 62, no.1, pp. 13-25. 1210-3195.

APA:
Wagner-Bojakowska, E., Wilczyński, W. (2015). Density topologies on the plane between ordinary and strong. II. Tatra Mountains Mathematical Publications, 62(1), 13-25. 1210-3195.