Axiom $T_D$ and the Simmons sublocale theorem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10404844" target="_blank" >RIV/00216208:11320/19:10404844 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jGRPsqk-1k" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jGRPsqk-1k</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/1213-7243.2019.030" target="_blank" >10.14712/1213-7243.2019.030</a>

Result language
angličtina
Original language name
Axiom $T_D$ and the Simmons sublocale theorem
Original language description
We are analyzing some of H. Simmons, S.B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom T_D for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. S.B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons' result. In this paper we show that the role of TD in this question is crucial. Concentration on the properties of TD-spaces and technique of sublocales in this context allows us to present a simple, transparent and choice-free proof of the scatteredness theorem.
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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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