Upper Porous Sets which are Not-σ-Lower Porous

Upper Porous Sets which are Not-σ-Lower Porous

Let X be a nonempty, topologically complete metric space with no isolated points. We show that there exists a closed upper porous set (in~a~strong sense) F\subset X which is not \s-lower porous (in a weak sense). More precisely, we show that there exists a closed (g_1)-shell porous set F\subset X wh...

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Veröffentlicht in:Real analysis exchange 2009, Vol.35 (no. 1), p.21-30
1. Verfasser: Koc, Martin
Format: Artikel
Sprache:eng
Schlagworte:
28A05
lower porosity
shell porosity
upper porosity
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Zusammenfassung:Let X be a nonempty, topologically complete metric space with no isolated points. We show that there exists a closed upper porous set (in~a~strong sense) F\subset X which is not \s-lower porous (in a weak sense). More precisely, we show that there exists a closed (g_1)-shell porous set F\subset X which is not \s-(g_2)-lower porous, where g_1 and~g_2 are arbitrary admissible functions.
ISSN:1930-1219