The Exact Borel Class Where a Density Completeness Axiom Holds

1991 ◽  
Vol 17 (1) ◽  
pp. 272
Author(s):  
Freiling ◽  
Humke
Keyword(s):  
Completeness Axiom ◽  
Borel Class

Some Remarks on Extreme Derivates

1969 ◽  
Vol 12 (4) ◽  
pp. 385-388 ◽  
Author(s):  
A. M. Bruckner
Keyword(s):  
Lipschitz Condition ◽  
Real Variable ◽  
Kernel Functions ◽  
Class 1 ◽  
Borel Class ◽  
Borel Measurable ◽  
Class Of Functions

In 1957 Hájek [1] proved that the extreme bilateral derivates of an arbitrary finite real valued function of a real variable, are Borel measurable of class ≦ 2. It was later shown by Staniszewska [3] that Hájek's result is the best possible (even among the class of functions satisfying a Lipschitz condition). Staniszewska exhibited a Eipschitz function whose extreme bilateral derivates are not in Borel class 1. Staniszewska's proof makes use of a result of Zahorski's [4] concerning kernel functions.

scholarly journals Computing Borel's regulator

2015 ◽  
Vol 27 (1) ◽  
Author(s):  
Zacky Choo ◽  
Wajid Mannan ◽  
Rubén J. Sánchez-García ◽  
Victor P. Snaith
Keyword(s):  
Infinite Series ◽  
Borel Class

AbstractWe present an infinite series formula based on the Karoubi–Hamida integral, for the universal Borel class evaluated on

scholarly journals Expected utility theory without the completeness axiom

2004 ◽  
Vol 115 (1) ◽  
pp. 118-133 ◽  
Author(s):  
Juan Dubra ◽  
Fabio Maccheroni ◽  
Efe A. Ok
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Completeness Axiom

scholarly journals Constructing Banaschewski compactification without Dedekind completeness axiom

2004 ◽  
Vol 2004 (69) ◽  
pp. 3799-3816
Author(s):  
S. K. Acharyya ◽  
K. C. Chattopadhyay ◽  
Partha Pratim Ghosh
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Open Problems ◽  
Structure Space ◽  
Ordered Field ◽  
Completeness Axiom ◽  
Dedekind Completeness ◽  
Stone Theorem ◽  
Stone’S Theorem

The main aim of this paper is to provide a construction of the Banaschewski compactification of a zero-dimensional Hausdorff topological space as a structure space of a ring of ordered field-valued continuous functions on the space, and thereby exhibit the independence of the construction from any completeness axiom for an ordered field. In the process of describing this construction we have generalized the classical versions of M. H. Stone's theorem, the Banach-Stone theorem, and the Gelfand-Kolmogoroff theorem. The paper is concluded with a conjecture of a split in the class of all zero-dimensional but not strongly zero-dimensional Hausdorff topological spaces into three classes that are labeled by inequalities between three compactifications ofX, namely, the Stone-Čech compactificationβX, the Banaschewski compactificationβ0X, and the structure space𝔐X,Fof the lattice-ordered commutative ringℭ(X,F)of all continuous functions onXtaking values in the ordered fieldF, equipped with its order topology. Some open problems are also stated.

scholarly journals On the Borel class of the derived set operator. II

1983 ◽  
Vol 79 ◽  
pp. 367-372 ◽  
Author(s):  
Douglas Cenzer ◽  
R. Daniel Mauldin
Keyword(s):  
Derived Set ◽  
Borel Class

A Borel reductibility theory for classes of countable structures

1989 ◽  
Vol 54 (3) ◽  
pp. 894-914 ◽  
Author(s):  
Harvey Friedman ◽  
Lee Stanley
Keyword(s):  
Point Of View ◽  
Algebraic Structures ◽  
Main Thrust ◽  
Similarity Type ◽  
Borel Class ◽  
Natural Classes

AbstractWe introduce a reducibility preordering between classes of countable structures, each class containing only structures of a given similarity type (which is allowed to vary from class to class). Though we sometimes work in a slightly larger context, we are principally concerned with the case where each class is an invariant Borel class (i.e. the class of all models, with underlying set = ω, of an Lω1ω sentence; from this point of view, the reducibility can be thought of as a (rather weak) sort of Lω1ω-interpretability notion). We prove a number of general results about this notion, but our main thrust is to situate various mathematically natural classes with respect to the preordering, most notably classes of algebraic structures such as groups and fields.

Structure of the Set of Norm-attaining Functionals on Strictly Convex Spaces

2011 ◽  
Vol 54 (2) ◽  
pp. 302-310 ◽  
Author(s):  
Ondřej Kurka
Keyword(s):  
Banach Space ◽  
Reflexive Banach Space ◽  
Strictly Convex ◽  
Borel Class ◽  
Norm Attaining ◽  
Convex Spaces

AbstractLet X be a separable non-reflexive Banach space. We show that there is no Borel class which contains the set of norm-attaining functionals for every strictly convex renorming of X.

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