Rercovering a compact Hausdorff space X from the compatibility ordering on C(X)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10393099" target="_blank" >RIV/00216208:11320/18:10393099 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xy8qI_e_ug" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xy8qI_e_ug</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/fm388-11-2017" target="_blank" >10.4064/fm388-11-2017</a>

Result language
angličtina
Original language name
Rercovering a compact Hausdorff space X from the compatibility ordering on C(X)
Original language description
Let f and g be scalar-valued, continuous functions on some topological space. We say that g dominates f in the compatibility ordering if g coincides with f on the support of f. We prove that two compact Hausdorff spaces are homeomorphic if and only if there exists a compatibility isomorphism between their families of scalar-valued, continuous functions. We derive the classical theorems of Gelfand-Kolmogorov, Milgram and Kaplansky as easy corollaries to our result, as well as a theorem of Jarosz [Bull. Canad. Math. Soc. 33 (1990)]. Sharp automatic-continuity results for compatibility isomorphisms are 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
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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