Displaying similar documents to “On Kantorovich's result on the symmetry of Dini derivatives”

Products of non- σ -lower porous sets

Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

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In the present article we provide an example of two closed non- σ -lower porous sets A , B ⊆ ℝ such that the product A × B is lower porous. On the other hand, we prove the following: Let X and Y be topologically complete metric spaces, let A ⊆ X be a non- σ -lower porous Suslin set and let B ⊆ Y be a non- σ -porous Suslin set. Then the product A × B is non- σ -lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non- σ -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.

The structure of the σ -ideal of σ -porous sets

Miroslav Zelený, Jan Pelant (2004)

Commentationes Mathematicae Universitatis Carolinae

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We show a general method of construction of non- σ -porous sets in complete metric spaces. This method enables us to answer several open questions. We prove that each non- σ -porous Suslin subset of a topologically complete metric space contains a non- σ -porous closed subset. We show also a sufficient condition, which gives that a certain system of compact sets contains a non- σ -porous element. Namely, if we denote the space of all compact subsets of a compact metric space E with the Vietoris...