Displaying similar documents to “Products of non-$\sigma $-lower porous sets”

σ -porosity is separably determined

Marek Cúth, Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

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We prove a separable reduction theorem for σ -porosity of Suslin sets. In particular, if A is a Suslin subset in a Banach space X , then each separable subspace of X can be enlarged to a separable subspace V such that A is σ -porous in X if and only if A ∩ V is σ -porous in V . Such a result is proved for several types of σ -porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend...

A σ -porous set need not be σ -bilaterally porous

R. J. Nájares, Luděk Zajíček (1994)

Commentationes Mathematicae Universitatis Carolinae

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A closed subset of the real line which is right porous but is not σ -left-porous is constructed.

On Kantorovich's result on the symmetry of Dini derivatives

Martin Koc, Luděk Zajíček (2010)

Commentationes Mathematicae Universitatis Carolinae

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For f : ( a , b ) → ℝ , let A f be the set of points at which f is Lipschitz from the left but not from the right. L.V. Kantorovich (1932) proved that, if f is continuous, then A f is a “( k d )-reducible set”. The proofs of L. Zajíček (1981) and B.S. Thomson (1985) give that A f is a σ -strongly right porous set for an arbitrary f . We discuss connections between these two results. The main motivation for the present note was the observation that Kantorovich’s result implies the existence of a σ -strongly right...