Almost disjoint families of countable sets and separable complementation properties
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F13%3A00391353" target="_blank" >RIV/67985840:_____/13:00391353 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2013.01.008" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2013.01.008</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2013.01.008" target="_blank" >10.1016/j.jmaa.2013.01.008</a>
Alternative languages
Result language
angličtina
Original language name
Almost disjoint families of countable sets and separable complementation properties
Original language description
We study the separable complementation property (SCP) and its natural variations in Banach spaces of continuous functions over compacta KA induced by almost disjoint families A of countable subsets of uncountable sets. For these spaces, we prove among other things that C(KA) has the controlled variant of the separable complementation property if and only if C(KA) is indelöf in the weak topology if and only if KA is monolithic. We give an example of A for which C(KA) has the SCP while KA is not monolithic and an example of a space C(KA) with controlled and continuous SCP which has neither a projectional skeleton nor a projectional resolution of the identity. Finally, we describe the structure of almost disjoint families of cardinality?1 which induce monolithic spaces of the form KA: they can be obtained from countably many ladder systems and pairwise disjoint families by applying simple operations.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
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Volume of the periodical
401
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
11
Pages from-to
939-949
UT code for WoS article
000315425900042
EID of the result in the Scopus database
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