Free monoids and generalized metric spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00113483" target="_blank" >RIV/00216224:14310/19:00113483 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0195669818300210" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0195669818300210</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2018.02.008" target="_blank" >10.1016/j.ejc.2018.02.008</a>

Result language
angličtina
Original language name
Free monoids and generalized metric spaces
Original language description
Let A be an ordered alphabet, A* be the free monoid over A ordered by the Higman ordering, and let F(A*) be the set of final segments of A*. With the operation of concatenation, this set is a monoid. We show that the submonoid F degrees(A*) := F(A*) {empty set} is free. The MacNeille completion N(A*) of A* is a submonoid of F(A*). As a corollary, we obtain that the monoid N degrees(A*) := N(A*) {empty set} is free. We give an interpretation of the freeness of F degrees(A*) in the category of metric spaces over the Heyting algebra V := F(A*), with the non-expansive mappings as morphisms. Each final segment F of A* yields the injective envelope S-F of a two-element metric space over V. The uniqueness of the decomposition of F is due to the uniqueness of the block decomposition of the graph G(F) associated to this injective envelope. (C) 2018 Elsevier Ltd. All rights reserved.
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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