On stable Baire classes
We introduce and study adhesive spaces. Using this concept we obtain a characterization of stable Baire maps f : X → Y of the class α for wide classes of topological spaces. In particular, we prove that for a topological space X and a contractible space Y a map f : X → Y belongs to the n th stable B...
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| Veröffentlicht in: | Acta mathematica Hungarica 2016-10, Vol.150 (1), p.36-48 |
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| container_title | Acta mathematica Hungarica |
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| creator | Karlova, O. Mykhaylyuk, V. |
| description | We introduce and study adhesive spaces. Using this concept we obtain a characterization of stable Baire maps
f
:
X
→
Y
of the class
α
for wide classes of topological spaces. In particular, we prove that for a topological space
X
and a contractible space
Y
a map
f
:
X
→
Y
belongs to the
n
th stable Baire class if and only if there exist a sequence
(
f
k
)
k
=
1
∞
of continuous maps
f
k
:
X
→
Y
and a sequence
(
F
k
)
k
=
1
∞
of functionally ambiguous sets of the
n
th class in
X
such that
f
|
F
k
=
f
k
|
F
k
for every
k
. Moreover, we show that every monotone function
f
:
R
→
R
is of the
α
th stable Baire class if and only if it belongs to the first stable Baire class. |
| doi_str_mv | 10.1007/s10474-016-0636-8 |
| format | Article |
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f
:
X
→
Y
of the class
α
for wide classes of topological spaces. In particular, we prove that for a topological space
X
and a contractible space
Y
a map
f
:
X
→
Y
belongs to the
n
th stable Baire class if and only if there exist a sequence
(
f
k
)
k
=
1
∞
of continuous maps
f
k
:
X
→
Y
and a sequence
(
F
k
)
k
=
1
∞
of functionally ambiguous sets of the
n
th class in
X
such that
f
|
F
k
=
f
k
|
F
k
for every
k
. Moreover, we show that every monotone function
f
:
R
→
R
is of the
α
th stable Baire class if and only if it belongs to the first stable Baire class.</description><identifier>ISSN: 0236-5294</identifier><identifier>EISSN: 1588-2632</identifier><identifier>DOI: 10.1007/s10474-016-0636-8</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Adhesives ; Continuity (mathematics) ; Mathematics ; Mathematics and Statistics</subject><ispartof>Acta mathematica Hungarica, 2016-10, Vol.150 (1), p.36-48</ispartof><rights>Akadémiai Kiadó, Budapest, Hungary 2016</rights><rights>Copyright Springer Science & Business Media 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-9d0daaa59793af9b04ea8e6bead852102ac01cb552ee67c3033903e8cdfee7bb3</citedby><cites>FETCH-LOGICAL-c316t-9d0daaa59793af9b04ea8e6bead852102ac01cb552ee67c3033903e8cdfee7bb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10474-016-0636-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10474-016-0636-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Karlova, O.</creatorcontrib><creatorcontrib>Mykhaylyuk, V.</creatorcontrib><title>On stable Baire classes</title><title>Acta mathematica Hungarica</title><addtitle>Acta Math. Hungar</addtitle><description>We introduce and study adhesive spaces. Using this concept we obtain a characterization of stable Baire maps
f
:
X
→
Y
of the class
α
for wide classes of topological spaces. In particular, we prove that for a topological space
X
and a contractible space
Y
a map
f
:
X
→
Y
belongs to the
n
th stable Baire class if and only if there exist a sequence
(
f
k
)
k
=
1
∞
of continuous maps
f
k
:
X
→
Y
and a sequence
(
F
k
)
k
=
1
∞
of functionally ambiguous sets of the
n
th class in
X
such that
f
|
F
k
=
f
k
|
F
k
for every
k
. Moreover, we show that every monotone function
f
:
R
→
R
is of the
α
th stable Baire class if and only if it belongs to the first stable Baire class.</description><subject>Adhesives</subject><subject>Continuity (mathematics)</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0236-5294</issn><issn>1588-2632</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1jz1PwzAURS0EEqEwI7ZIzIZnO_4aoaKAVKkLzJbtvKBWISl2OvDvcRUGFqYnXd1znw4hNwzuGIC-zwwa3VBgioISipoTUjFpDOVK8FNSAS-h5LY5Jxc57wBACmgqcr0Z6jz50GP96LcJ69j7nDFfkrPO9xmvfu-CvK-e3pYvdL15fl0-rGkUTE3UttB676XVVvjOBmjQG1QBfWskZ8B9BBaDlBxR6ShACAsCTWw7RB2CWJDbeXefxq8D5sntxkMaykvHjAGjNShbWmxuxTTmnLBz-7T99OnbMXBHfzf7u-Lvjv7OFIbPTC7d4QPTn-V_oR-KFFul</recordid><startdate>20161001</startdate><enddate>20161001</enddate><creator>Karlova, O.</creator><creator>Mykhaylyuk, V.</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20161001</creationdate><title>On stable Baire classes</title><author>Karlova, O. ; Mykhaylyuk, V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-9d0daaa59793af9b04ea8e6bead852102ac01cb552ee67c3033903e8cdfee7bb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Adhesives</topic><topic>Continuity (mathematics)</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Karlova, O.</creatorcontrib><creatorcontrib>Mykhaylyuk, V.</creatorcontrib><collection>CrossRef</collection><jtitle>Acta mathematica Hungarica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Karlova, O.</au><au>Mykhaylyuk, V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On stable Baire classes</atitle><jtitle>Acta mathematica Hungarica</jtitle><stitle>Acta Math. Hungar</stitle><date>2016-10-01</date><risdate>2016</risdate><volume>150</volume><issue>1</issue><spage>36</spage><epage>48</epage><pages>36-48</pages><issn>0236-5294</issn><eissn>1588-2632</eissn><abstract>We introduce and study adhesive spaces. Using this concept we obtain a characterization of stable Baire maps
f
:
X
→
Y
of the class
α
for wide classes of topological spaces. In particular, we prove that for a topological space
X
and a contractible space
Y
a map
f
:
X
→
Y
belongs to the
n
th stable Baire class if and only if there exist a sequence
(
f
k
)
k
=
1
∞
of continuous maps
f
k
:
X
→
Y
and a sequence
(
F
k
)
k
=
1
∞
of functionally ambiguous sets of the
n
th class in
X
such that
f
|
F
k
=
f
k
|
F
k
for every
k
. Moreover, we show that every monotone function
f
:
R
→
R
is of the
α
th stable Baire class if and only if it belongs to the first stable Baire class.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10474-016-0636-8</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0236-5294 |
| ispartof | Acta mathematica Hungarica, 2016-10, Vol.150 (1), p.36-48 |
| issn | 0236-5294 1588-2632 |
| language | eng |
| recordid | cdi_proquest_journals_1880877069 |
| source | SpringerNature Journals |
| subjects | Adhesives Continuity (mathematics) Mathematics Mathematics and Statistics |
| title | On stable Baire classes |
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