scholarly journals On zero-dimensional Milutin maps and Michael selection theorems

1993 ◽  
Vol 54 (1-3) ◽  
pp. 77-83 ◽  
Author(s):  
D. Repovš ◽  
P.V. Semenov ◽  
E.V. Ščepin
Keyword(s):  
Selection Theorems

scholarly journals Countable sections for locally compact group actions

1992 ◽  
Vol 12 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Alexander S. Kechris
Keyword(s):  
Compact Group ◽  
Equivalence Relation ◽  
Group Actions ◽  
Locally Compact Group ◽  
Borel Space ◽  
Locally Compact ◽  
Borel Equivalence Relation ◽  
Measurable Section ◽  
Singular Action

AbstractIt has been shown by J. Feldman, P. Hahn and C. C. Moore that every non-singular action of a second countable locally compact group has a countable (in fact so-called lacunary) complete measurable section. This is extended here to the purely Borel theoretic category, consisting of a Borel action of such a group on an analytic Borel space (without any measure). Characterizations of when an arbitrary Borel equivalence relation admits a countable complete Borel section are also established.

Selection Theorems for Nonconvex-Valued Maps

1998 ◽  
pp. 173-185
Author(s):  
Dušan Repovš ◽  
Pavel Vladimirovič Semenov
Keyword(s):  
Selection Theorems

Unified Selection Theorems

1998 ◽  
pp. 155-159
Author(s):  
Dušan Repovš ◽  
Pavel Vladimirovič Semenov
Keyword(s):  
Selection Theorems

scholarly journals The Borel structure of iterates of continuous functions

1989 ◽  
Vol 32 (3) ◽  
pp. 483-494 ◽  
Author(s):  
Paul D. Humke ◽  
M. Laczkovich
Keyword(s):  
Banach Space ◽  
Continuous Functions ◽  
Baire Space ◽  
Space Of Continuous Functions ◽  
Borel Structure ◽  
Image Position ◽  
Set Of Points ◽  
Positive Integers

Let C[0,1] be the Banach space of continuous functions defined on [0,1] and let C be the set of functions f∈C[0,1] mapping [0,1] into itself. If f∈C, fk will denote the kth iterate of f and we put Ck = {fk:f∈C;}. The set of increasing (≡ nondecreasing) and decreasing (≡ nonincreasing) functions in C will be denoted by ℐ and D, respectively. If a function f is defined on an interval I, we let C(f) denote the set of points at which f is locally constant, i.e.We let N denote the set of positive integers and NN denote the Baire space of sequences of positive integers.

Local paraconvexity and local selection theorems

1999 ◽  
Vol 65 (2) ◽  
pp. 214-220
Author(s):  
P. V. Semenov
Keyword(s):  
Local Selection ◽  
Selection Theorems
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