The structure of the $\sigma $-ideal of $\sigma $-porous sets

Miroslav Zelený; Jan Pelant

Displaying similar documents to “The structure of the $σ$ -ideal of $σ$ -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 $A \cap V$ 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...

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 $A, B \subseteq ℝ$ such that the product $A \times B$ is lower porous. On the other hand, we prove the following: Let $X$ and $Y$ be topologically complete metric spaces, let $A \subseteq X$ be a non- $σ$ -lower porous Suslin set and let $B \subseteq Y$ be a non- $σ$ -porous Suslin set. Then the product $A \times B$ 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...

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 $f : (a, b) \to ℝ$ , 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...

Displaying similar documents to “The structure of the σ -ideal of σ -porous sets”

σ -porosity is separably determined

Products of non- σ -lower porous sets

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

On Kantorovich's result on the symmetry of Dini derivatives

Displaying similar documents to “The structure of the $σ$ -ideal of $σ$ -porous sets”

$σ$ -porosity is separably determined

Products of non- $σ$ -lower porous sets

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