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2 Journal of Applied Analysis

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Contrasting symmetric porosity and porosity

100%

Evans M. J. , Humke P. D.

Journal of Applied Analysis

1998

tom Vol. 4, nr 1

19-41

It is known that the following two fundamental properties of porosity fail for symmetric porosity: 1) Every nowhere dense set A contains a residual subset of points x at which A has porosity 1. 2) If A is a porous set and 0 < p < 1, then A can be written as a countable union of sets, each of which has porosity at least p at each of its points. Here we explore the somewhat surprising extent to which these properties fail to carry over to the symmetric setting and investigate what symmetric analogs do hold.

On symmetrically porouscontinuous functions

75%

Kowalczyk S. , Turowska M.

tom Vol. 22, nr 2

141--151

In the present paper, we introduce the notion of symmetrically porouscontinuous functions. We investigate some properties of symmetric porouscontinuity and its connections with the notion of porouscontinuity, studied by Borsík and Holos in [2]. We prove that there are 2c symmetrically porouscontinuous functions, which extends results of [1] concerning ρ-upper continuous functions.