Displaying similar documents to “Inscribing closed non- σ -lower porous sets into Suslin non- σ -lower porous sets.”

Inscribing compact non-σ-porous sets into analytic non-σ-porous sets

Miroslav Zelený, Luděk Zajíček (2005)

Fundamenta Mathematicae

Similarity:

The main aim of this paper is to give a simpler proof of the following assertion. Let A be an analytic non-σ-porous subset of a locally compact metric space, E. Then there exists a compact non-σ-porous subset of A. Moreover, we prove the above assertion also for σ-P-porous sets, where P is a porosity-like relation on E satisfying some additional conditions. Our result covers σ-⟨g⟩-porous sets, σ-porous sets, and σ-symmetrically porous sets.

Products of non- σ -lower porous sets

Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

Similarity:

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

Similarity:

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...