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2007/2008 The Intersection Conditions for <s>-Density Systems of Paths
Anna Loranty
Real Anal. Exchange 33(1): 41-50 (2007/2008).


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.


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Anna Loranty. "The Intersection Conditions for <s>-Density Systems of Paths." Real Anal. Exchange 33 (1) 41 - 50, 2007/2008.


Published: 2007/2008
First available in Project Euclid: 28 April 2008

MathSciNet: MR2402862

Primary: 26A21 , 54A10

Keywords: approximately continuous function , density topology , intersection conditions , system of paths

Rights: Copyright © 2007 Michigan State University Press

Vol.33 • No. 1 • 2007/2008
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