Real Analysis Exchange

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

Anna Loranty

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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

Subjects
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)

Keywords
density topology system of paths intersection conditions approximately continuous function

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


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