## Real Analysis Exchange

### The Intersection Conditions for <s>-Density Systems of Paths

Anna Loranty

#### Abstract

We investigate the intersection conditions for an $\s$-density system of paths. We show, for example, that for every unbounded and nondecreasing sequence of positive numbers $\s$ such that $\liminf_{n\rightarrow \infty }\frac{s_n}{s_{n+1}} =0$, there exists a system of paths connected with $\s$-density points which does not satisfy the intersection conditions. Moreover, we show that a function $f\:mathbb{R}\rightarrow \mathbb{R}$ is $\s$-approximately continuous if and only if $f$ is continuous with respect to some $\s$-density system of paths.

#### Article information

Source
Real Anal. Exchange, Volume 33, Number 1 (2007), 41-50.

Dates
First available in Project Euclid: 28 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1209398377

Mathematical Reviews number (MathSciNet)
MR2402862

#### Citation

Loranty, Anna. The Intersection Conditions for &lt; s &gt;-Density Systems of Paths. Real Anal. Exchange 33 (2007), no. 1, 41--50. https://projecteuclid.org/euclid.rae/1209398377