Compact covering mappings and cofinal families of compact subsets of a Borel set

G. Debs, and J. Saint Raymond. "Compact covering mappings and cofinal families of compact subsets of a Borel set." Fundamenta Mathematicae 167.3 (2001): 213-249. <http://eudml.org/doc/282246>.

@article{G2001,
abstract = {Among other results we prove that the topological statement “Any compact covering mapping between two Π⁰₃ spaces is inductively perfect” is equivalent to the set-theoretical statement "$∀α ∈ ω^\{ω\}, ω₁^\{L(α)\} < ω₁$"; and that the statement “Any compact covering mapping between two coanalytic spaces is inductively perfect” is equivalent to “Analytic Determinacy”. We also prove that these statements are connected to some regularity properties of coanalytic cofinal sets in (X), the hyperspace of all compact subsets of a Borel set X.},
author = {G. Debs, J. Saint Raymond},
journal = {Fundamenta Mathematicae},
keywords = {compact covering mapping; spaces; inductively perfect; coanalytic spaces; analytic determinacy; regularity; coanalytic cofinal sets; compact subsets of a Borel set},
language = {eng},
number = {3},
pages = {213-249},
title = {Compact covering mappings and cofinal families of compact subsets of a Borel set},
url = {http://eudml.org/doc/282246},
volume = {167},
year = {2001},
}

TY - JOUR
AU - G. Debs
AU - J. Saint Raymond
TI - Compact covering mappings and cofinal families of compact subsets of a Borel set
JO - Fundamenta Mathematicae
PY - 2001
VL - 167
IS - 3
SP - 213
EP - 249
AB - Among other results we prove that the topological statement “Any compact covering mapping between two Π⁰₃ spaces is inductively perfect” is equivalent to the set-theoretical statement "$∀α ∈ ω^{ω}, ω₁^{L(α)} < ω₁$"; and that the statement “Any compact covering mapping between two coanalytic spaces is inductively perfect” is equivalent to “Analytic Determinacy”. We also prove that these statements are connected to some regularity properties of coanalytic cofinal sets in (X), the hyperspace of all compact subsets of a Borel set X.
LA - eng
KW - compact covering mapping; spaces; inductively perfect; coanalytic spaces; analytic determinacy; regularity; coanalytic cofinal sets; compact subsets of a Borel set
UR - http://eudml.org/doc/282246
ER -