On embedding separable spaces C(L) in arbitrary spaces C(K)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00389465" target="_blank" >RIV/68407700:21230/25:00389465 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s43037-025-00439-0" target="_blank" >https://doi.org/10.1007/s43037-025-00439-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s43037-025-00439-0" target="_blank" >10.1007/s43037-025-00439-0</a>

Result language
angličtina
Original language name
On embedding separable spaces C(L) in arbitrary spaces C(K)
Original language description
Supplementing and expanding classical results, for compact spaces K and L, L metric, and their Banach spaces C(L) and C(K) of continuous real-valued functions, we provide several characterizations of the existence of isometric, resp. isomorphic, embeddings of C(L) into C(K). In particular, we show that if the embedded space C(L) is separable, then the classical theorems of Holsztynski and Gordon become equivalences. We also obtain new results describing the relative cellularities of the perfect kernel of a given compact space K and of the Cantor-Bendixson derived sets of K of countable order in terms of the presence of isometric copies of specific spaces C(L) inside C(K).
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)