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Mathematics  2012 

On the nonexistence of a relation between σ-left-porosity and σ-right-porosity

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Abstract:

Given an arbitrarily weak notion of left--porosity and an arbitrarily strong notion of right--porosity, we construct an example of closed subset of the real line which is not sigma-left--porous and is right--porous. We also briefly summarize the relations between three different definitions of porosity controlled by a function; we then observe that our construction gives the example for any combination of these definitions of left-porosity and right-porosity.

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