Restricting uniformly open surjections

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00480050" target="_blank" >RIV/67985840:_____/17:00480050 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/17:10368191
Result on the web
<a href="http://dx.doi.org/10.1016/j.crma.2017.09.008" target="_blank" >http://dx.doi.org/10.1016/j.crma.2017.09.008</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.crma.2017.09.008" target="_blank" >10.1016/j.crma.2017.09.008</a>

Result language
angličtina
Original language name
Restricting uniformly open surjections
Original language description
We employ the theory of elementary submodels to improve a recent result by Aron, Jaramillo and Le Donne (2017) [1] concerning restricting uniformly open, continuous surjections to smaller subspaces where they remain surjective. To wit, suppose that X and Y are metric spaces and let f:X...Y be a continuous surjection. If X is complete and f is uniformly open, then X contains a closed subspace Z with the same density as Y such that f restricted to Z is still uniformly open and surjective. Moreover, if X is a Banach space, then Z may be taken to be a closed linear subspace. A counterpart of this theorem for uniform spaces is also established.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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