Uniformities and a quantale structure on localic groups

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455257" target="_blank" >RIV/00216208:11320/22:10455257 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Mi.KrpkLR7" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Mi.KrpkLR7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.36045/j.bbms.210823" target="_blank" >10.36045/j.bbms.210823</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Uniformities and a quantale structure on localic groups

Popis výsledku v původním jazyce

Similarly like classical topological groups, the point-free counterparts, localic groups, possess natural uniformities (see e.g. [4,2,10]) obtained from an involutive binary operation on L (roughly corresponding to the algebra of subsets of a classical group). It is the operation that naturally induces the uniformities (even if it would not result from a group) and a study of this aspect of the construction is the main topic of this article. We have here a functor associating with the localic groups quantales of a special type (and with frame group homomorphisms quantale homomorphisms) which are shown to create the uniformities, in fact as a special case of the natural uniformities connected with metric structures. Also, we present a condition under which the quantale allows a reconstruction of the localic group.

Název v anglickém jazyce

Uniformities and a quantale structure on localic groups

Popis výsledku anglicky

Similarly like classical topological groups, the point-free counterparts, localic groups, possess natural uniformities (see e.g. [4,2,10]) obtained from an involutive binary operation on L (roughly corresponding to the algebra of subsets of a classical group). It is the operation that naturally induces the uniformities (even if it would not result from a group) and a study of this aspect of the construction is the main topic of this article. We have here a functor associating with the localic groups quantales of a special type (and with frame group homomorphisms quantale homomorphisms) which are shown to create the uniformities, in fact as a special case of the natural uniformities connected with metric structures. Also, we present a condition under which the quantale allows a reconstruction of the localic group.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Bulletin of the Belgian Mathematical Society - Simon Stevin

ISSN

1370-1444

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

BE - Belgické království

Počet stran výsledku

18

Strana od-do

561-578

Kód UT WoS článku

000996708000005

EID výsledku v databázi Scopus

2-s2.0-85161989389