On Kantorovich's result on the symmetry of Dini derivatives

Martin Koc; Luděk Zajíček

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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 $A, B \subseteq ℝ$ 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...

$σ$ -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...

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.

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

Products of non- σ -lower porous sets

σ -porosity is separably determined

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

Products of non- $σ$ -lower porous sets

$σ$ -porosity is separably determined

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