On projective mappings

S. S. Gabrielyan

doi:10.1023/A:1020597801906

On projective mappings

S. S. Gabrielyan

Research output: Contribution to journal › Article › peer-review

Abstract

Let X, Y be Polish spaces, and let B_k be the σ-algebra generated by the projective class L_2k+1. A mapping f: X → Y is called k-projective if f^-1(E) ∈ B_k for any Borel subset E ⊂ Y. The following theorem is our main result: for any k-projective mapping f: X → Y there exist a Polish space X_S, a dense subset X_S ∈ B_k, and two continuous mappings f0, i: X_S → Y such that i) fo|X_S = f ○ i|X _S; ii) i|X_S is a bijection.

Original language	English
Pages (from-to)	295-300
Number of pages	6
Journal	Mathematical Notes
Volume	72
Issue number	3-4
DOIs	https://doi.org/10.1023/A:1020597801906
State	Published - 1 Jan 2002
Externally published	Yes

Keywords

Borel mapping
Borel subset
Polish space
k-projective mapping

ASJC Scopus subject areas

General Mathematics

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10.1023/A:1020597801906

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title = "On projective mappings",

abstract = "Let X, Y be Polish spaces, and let Bk be the σ-algebra generated by the projective class L2k+1. A mapping f: X → Y is called k-projective if f-1(E) ∈ Bk for any Borel subset E ⊂ Y. The following theorem is our main result: for any k-projective mapping f: X → Y there exist a Polish space XS, a dense subset XS ∈ Bk, and two continuous mappings f0, i: XS → Y such that i) fo|XS = f ○ i|X S; ii) i|XS is a bijection.",

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N2 - Let X, Y be Polish spaces, and let Bk be the σ-algebra generated by the projective class L2k+1. A mapping f: X → Y is called k-projective if f-1(E) ∈ Bk for any Borel subset E ⊂ Y. The following theorem is our main result: for any k-projective mapping f: X → Y there exist a Polish space XS, a dense subset XS ∈ Bk, and two continuous mappings f0, i: XS → Y such that i) fo|XS = f ○ i|X S; ii) i|XS is a bijection.

AB - Let X, Y be Polish spaces, and let Bk be the σ-algebra generated by the projective class L2k+1. A mapping f: X → Y is called k-projective if f-1(E) ∈ Bk for any Borel subset E ⊂ Y. The following theorem is our main result: for any k-projective mapping f: X → Y there exist a Polish space XS, a dense subset XS ∈ Bk, and two continuous mappings f0, i: XS → Y such that i) fo|XS = f ○ i|X S; ii) i|XS is a bijection.

KW - Borel mapping

KW - Borel subset

KW - Polish space

KW - k-projective mapping

UR - https://www.scopus.com/pages/publications/0141848659

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SP - 295

EP - 300

JO - Mathematical Notes

JF - Mathematical Notes

IS - 3-4

ER -

On projective mappings

Abstract

Keywords

ASJC Scopus subject areas

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