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Licensed Unlicensed Requires Authentication Published by De Gruyter June 4, 2010

Contrasting Symmetric Porosity and Porosity

  • M. J. Evans and P. D. Humke


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.

Key words and phrases.: Symmetric porosity; porosity
Received: 1996-12-16
Revised: 1997-08-14
Published Online: 2010-06-04
Published in Print: 1998-June

© Heldermann Verlag

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