scholarly journals Universally meager sets and principles of generic continuity and selection in Banach spaces

2007 ◽  
Vol 208 (1) ◽  
pp. 274-298 ◽  
Author(s):  
Stevo Todorcevic
Keyword(s):  
Banach Spaces ◽  
Meager Sets ◽  
Generic Continuity

scholarly journals SOME EXAMPLES OF MEAGER SETS IN BANACH SPACES

2000 ◽  
Vol 26 (2) ◽  
pp. 877 ◽  
Author(s):  
Balcerzak ◽  
Wachowicz
Keyword(s):  
Banach Spaces ◽  
Meager Sets

scholarly journals Generic continuity of minimal set-valued mappings

1997 ◽  
Vol 63 (2) ◽  
pp. 238-262 ◽  
Author(s):  
W. B. Moors ◽  
J. R. Giles
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Metric Space ◽  
Complete Metric Space ◽  
Minimal Set ◽  
Set Valued Mapping ◽  
Set Valued Mappings ◽  
Permanence Properties ◽  
Generic Continuity ◽  
Sufficiency Conditions

AbstractWe study classes of Banach spaces where every set-valued mapping from a complete metric space into subsets of the Banach space which satisfies certain minimal properties, is single-valued and norm upper semi-continuous at the points of a dense Gδ subset of its domain. Characterisations of these classes are developed and permanence properties are established. Sufficiency conditions for membership of these classes are defined in terms of fragmentability and σ-fragmentability of the weak topology. A characterisation of non membership is used to show that l∞ (N) is not a member of our classe of generic continuity spaces.

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