Real Analysis Exchange

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

Anna Loranty

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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

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

First available in Project Euclid: 28 April 2008

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Mathematical Reviews number (MathSciNet)

Primary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)

density topology system of paths intersection conditions approximately continuous function


Loranty, Anna. The Intersection Conditions for &lt; s &gt;-Density Systems of Paths. Real Anal. Exchange 33 (2007), no. 1, 41--50.

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