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DECOMPOSING FUNCTIONS OF BAIRE CLASS $2$ ON POLISH SPACES

Part of: Real functions Connections with other structures, applications Set theory

Published online by Cambridge University Press:  26 October 2020

LONGYUN DING ,
TAKAYUKI KIHARA ,
BRIAN SEMMES  and
JIAFEI ZHAO
LONGYUN DING
Affiliation:
SCHOOL OF MATHEMATICAL SCIENCES AND LPMC NANKAI UNIVERSITYTIANJIN, 300071, P.R. CHINAE-mail: [email protected]: [email protected]
TAKAYUKI KIHARA
Affiliation:
GRADUATE SCHOOL OF INFORMATICS NAGOYA UNIVERSITYNAGOYA, 464-8601, JAPANE-mail: [email protected]
BRIAN SEMMES
Affiliation:
STUDYLAB LANGUAGE SCHOOL MOSCOW, NIKOLSKAYA ST. 10, NIKOLSKAYA PLAZA OFFICE CENTRE RUSSIAN FEDERATIONE-mail: [email protected]
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Abstract

We prove the Decomposability Conjecture for functions of Baire class $2$ from a Polish space to a separable metrizable space. This partially answers an important open problem in descriptive set theory.

Keywords

Decomposability ConjectureJayne-Rogers Theoremfunctions of Baire class 2

MSC classification

Primary: 03E15: Descriptive set theory
Secondary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 26A21: Classification of real functions; Baire classification of sets and functions
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 3 , September 2020 , pp. 960 - 971
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Copyright
© The Association for Symbolic Logic 2020

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References

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