On an aspect of scatteredness in the point-free setting

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10330656" target="_blank" >RIV/00216208:11320/16:10330656 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4171/PM/1980" target="_blank" >http://dx.doi.org/10.4171/PM/1980</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4171/PM/1980" target="_blank" >10.4171/PM/1980</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On an aspect of scatteredness in the point-free setting

Popis výsledku v původním jazyce

It is well known that a locale is subfit iff each of its open sublocales is a join of closed ones, and fit iff each of its closed sublocales is a meet of open ones. This formulation, however, exaggerates the parallelism between the behavior of fitness and subfitness. For it can be shown that a locale is fit iff each of its sublocales is a meet of closed ones, but it is not the case that a locale is subfit iff each of its sublocales is a join of closed ones. Thus we are led to take up the very natural question of which locales have the feature that every sublocale is a join of closed sublocales. In this note we show that these are precisely the subfit locales which are scattered in the point-free sense of [13], and we add a variation for spatial frames.

Název v anglickém jazyce

On an aspect of scatteredness in the point-free setting

Popis výsledku anglicky

It is well known that a locale is subfit iff each of its open sublocales is a join of closed ones, and fit iff each of its closed sublocales is a meet of open ones. This formulation, however, exaggerates the parallelism between the behavior of fitness and subfitness. For it can be shown that a locale is fit iff each of its sublocales is a meet of closed ones, but it is not the case that a locale is subfit iff each of its sublocales is a join of closed ones. Thus we are led to take up the very natural question of which locales have the feature that every sublocale is a join of closed sublocales. In this note we show that these are precisely the subfit locales which are scattered in the point-free sense of [13], and we add a variation for spatial frames.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Portugaliae Mathematica

ISSN

0032-5155

e-ISSN

—

Svazek periodika

73

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

PT - Portugalská republika

Počet stran výsledku

14

Strana od-do

139-152

Kód UT WoS článku

000377323000003

EID výsledku v databázi Scopus

2-s2.0-84962861173