Efimov spaces and the separable quotient problem for spaces C-P(K)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00480123" target="_blank" >RIV/67985840:_____/18:00480123 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2017.08.010" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2017.08.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2017.08.010" target="_blank" >10.1016/j.jmaa.2017.08.010</a>

Result language
angličtina
Original language name
Efimov spaces and the separable quotient problem for spaces C-P(K)
Original language description
The classic Rosenthal-Lacey theorem asserts that the Banach space C(K)of continuous real-valued maps on an infinite compact space K has a quotient isomorphic to c or ...2. More recently, Kakol and Saxon [20] proved that the space Cp(K) endowed with the pointwise topology has an infinite-dimensional separable quotient algebra iff K has an infinite countable closed subset. Hence Cp(betaN) lacks infinite-dimensional separable quotient algebras. This motivates the following question: (...) Does Cp(K) admit an infinite-dimensional separable quotient (shortly SQ) for any infinite compact space K? Particularly, does Cp(betaN) admit SQ? Our main theorem implies that Cp(K) has SQ for any compact space K containing a copy of betaN. Consequently, this result reduces problem (...) to the case when K is an Efimov space (i.e. K is an infinite compact space that contains neither a non-trivial convergent sequence nor a copy of betaN).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF16-34860L" target="_blank" >GF16-34860L: Logic and Topology in Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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