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

Fundamenta Mathematicae (2001)

- Volume: 167, Issue: 3, page 213-249
- ISSN: 0016-2736

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topG. 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 -

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