A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions

We offer a new and simpler proof of a recent ϵ-δ characterization of Baire class one functions using a theorem by Henri Lebesgue. The proof is more elementary in the sense that it does not use the Baire Category Theorem. Furthermore, the proof requires only that the domain and range be separable met...

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Main Authors:	Cabral, Emmanuel A, Fenecios, Jonald P
Format:	text
Published:	Archīum Ateneo 2015
Subjects:	Baire class one function oscillation of a function Polish spaces separable metric spaces Mathematics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/62 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1061&context=mathematics-faculty-pubs
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Institution:	Ateneo De Manila University

id	ph-ateneo-arc.mathematics-faculty-pubs-1061
record_format	eprints
spelling	ph-ateneo-arc.mathematics-faculty-pubs-10612020-03-13T06:39:04Z A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions Cabral, Emmanuel A Fenecios, Jonald P We offer a new and simpler proof of a recent ϵ-δ characterization of Baire class one functions using a theorem by Henri Lebesgue. The proof is more elementary in the sense that it does not use the Baire Category Theorem. Furthermore, the proof requires only that the domain and range be separable metric spaces instead of Polish spaces. 2015-01-01T08:00:00Z text application/pdf https://archium.ateneo.edu/mathematics-faculty-pubs/62 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1061&context=mathematics-faculty-pubs Mathematics Faculty Publications Archīum Ateneo Baire class one function oscillation of a function Polish spaces separable metric spaces Mathematics
institution	Ateneo De Manila University
building	Ateneo De Manila University Library
country	Philippines
collection	archium.Ateneo Institutional Repository
topic	Baire class one function oscillation of a function Polish spaces separable metric spaces Mathematics
spellingShingle	Baire class one function oscillation of a function Polish spaces separable metric spaces Mathematics Cabral, Emmanuel A Fenecios, Jonald P A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions
description	We offer a new and simpler proof of a recent ϵ-δ characterization of Baire class one functions using a theorem by Henri Lebesgue. The proof is more elementary in the sense that it does not use the Baire Category Theorem. Furthermore, the proof requires only that the domain and range be separable metric spaces instead of Polish spaces.
format	text
author	Cabral, Emmanuel A Fenecios, Jonald P
author_facet	Cabral, Emmanuel A Fenecios, Jonald P
author_sort	Cabral, Emmanuel A
title	A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions
title_short	A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions
title_full	A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions
title_fullStr	A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions
title_full_unstemmed	A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions
title_sort	simpler proof for the ϵ-δ characterization of baire class one functions
publisher	Archīum Ateneo
publishDate	2015
url	https://archium.ateneo.edu/mathematics-faculty-pubs/62 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1061&context=mathematics-faculty-pubs
_version_	1681506545934794752

A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions

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