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The main aim of this paper is to prove that everynon-σ-lower porous Suslin set in a topologically completemetric space contains a closed non-σ-lower porous  subset.In fact, we prove a general result of this type on “abstractporosities.” This general theorem is also applied to ball smallsets in Hilbert spaces and to σ-cone-supported sets in separable Banach spaces

abstract and applied analysis

Inscribing closed non-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\sigma$" id="E1"><mml:mi>σ</mml:mi></mml:math>-lower porous sets into Suslin non-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\sigma$" id="E2"><mml:mi>σ</mml:mi></mml:math>-lower porous sets

Inscribing closed non-σ-lower porous sets into Suslin non-σ-lower porous sets