THE STRUCTURE OF THE σ-IDEAL OF σ-POROUS SETS

1999 ◽  
Vol 25 (1) ◽  
pp. 87
Author(s):  
Zelený
Keyword(s):  
Porous Sets

scholarly journals Unions and ideals of locally strongly porous sets

2017 ◽  
Vol 41 ◽  
pp. 1510-1534
Author(s):  
Maya ALTINOK ◽  
Oleksiy DOVGOSHEY ◽  
Mehmet KÜÇÜKASLAN
Keyword(s):  
Porous Sets

Fr ´Echet Differentiability Except For Γ‎-Null Sets

2012 ◽  
Author(s):  
Joram Lindenstrauss ◽  
David Preiss ◽  
Tiˇser Jaroslav
Keyword(s):  
Banach Spaces ◽  
Common Point ◽  
Lipschitz Functions ◽  
Infinite Dimensional ◽  
Lipschitz Maps ◽  
Almost Everywhere ◽  
Fréchet Differentiability ◽  
Gateaux Derivatives ◽  
Frechet Differentiability ◽  
Porous Sets

This chapter gives an account of the known genuinely infinite dimensional results proving Fréchet differentiability almost everywhere except for Γ‎-null sets. Γ‎-null sets provide the only notion of negligible sets with which a Fréchet differentiability result is known. Porous sets appear as sets at which Gâteaux derivatives can behave irregularly, and they turn out to be the only obstacle to validity of a Fréchet differentiability result Γ‎-almost everywhere. Furthermore, geometry of the space may (or may not) guarantee that porous sets are Γ‎-null. The chapter also shows that on some infinite dimensional Banach spaces countable collections of real-valued Lipschitz functions, and even of fairly general Lipschitz maps to infinite dimensional spaces, have a common point of Fréchet differentiability.

scholarly journals Cardinal invariants of strongly porous sets

2017 ◽  
pp. 1-16
Author(s):  
Osvaldo Guzmán ◽  
Michael Hrušák ◽  
Arturo Martinez-Celis
Keyword(s):  
Cardinal Invariants ◽  
Porous Sets

ON UNIONS OF POROUS SETS

1996 ◽  
Vol 22 (1) ◽  
pp. 74
Author(s):  
Wojdowski
Keyword(s):  
Porous Sets
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