Adjoint maps between implicative semilattices and continuity of localic maps

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455252" target="_blank" >RIV/00216208:11320/22:10455252 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rvxyB97Sg6" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rvxyB97Sg6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00012-022-00767-4" target="_blank" >10.1007/s00012-022-00767-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Adjoint maps between implicative semilattices and continuity of localic maps

Popis výsledku v původním jazyce

We study residuated homomorphisms (r-morphisms) and their adjoints, the so-called localizations (or l-morphisms), between implicative semilattices, because these objects may be characterized as semilattices whose unary meet operations have adjoints. Since left resp. right adjoint maps are the residuated resp. residual maps (having the property that preimages of principal downsets resp. upsets are again such), one may not only regard the l-morphisms as abstract continuous maps in a pointfree framework (as familiar in the complete case), but also characterize them by concrete closure-theoretical continuity properties. These concepts apply to locales (frames, complete Heyting lattices) and provide generalizations of continuous and open maps between spaces to an algebraic (not necessarily complete) pointfree setting.

Název v anglickém jazyce

Adjoint maps between implicative semilattices and continuity of localic maps

Popis výsledku anglicky

We study residuated homomorphisms (r-morphisms) and their adjoints, the so-called localizations (or l-morphisms), between implicative semilattices, because these objects may be characterized as semilattices whose unary meet operations have adjoints. Since left resp. right adjoint maps are the residuated resp. residual maps (having the property that preimages of principal downsets resp. upsets are again such), one may not only regard the l-morphisms as abstract continuous maps in a pointfree framework (as familiar in the complete case), but also characterize them by concrete closure-theoretical continuity properties. These concepts apply to locales (frames, complete Heyting lattices) and provide generalizations of continuous and open maps between spaces to an algebraic (not necessarily complete) pointfree setting.

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

Algebra Universalis

ISSN

0002-5240

e-ISSN

1420-8911

Svazek periodika

83

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

13

Kód UT WoS článku

000770767700002

EID výsledku v databázi Scopus

2-s2.0-85126816202