Lindelof tightness and the Dedekind-MacNeille completion of a regular sigma-frame

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10368629" target="_blank" >RIV/00216208:11320/17:10368629 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.2989/16073606.2017.1288665" target="_blank" >http://dx.doi.org/10.2989/16073606.2017.1288665</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2989/16073606.2017.1288665" target="_blank" >10.2989/16073606.2017.1288665</a>

Result language

angličtina

Original language name

Lindelof tightness and the Dedekind-MacNeille completion of a regular sigma-frame

Original language description

Tightness is a notion that arose in an attempt to understand the reverse reflection problem: given a monoreflection of a category onto a subcategory, determine which subobjects of an object in the subcategory reflect to it; those which do are termed tight. Thus tightness can be seen as a strong density property. We present an analysis of lambda-tightness, tightness with respect to the localic Lindeldof reflection. Leading to this analysis, we prove that the normal, or Dedekind-MacNeille, completion of a regular sigma-frame A is a frame. Moreover, the embedding of A in its normal completion is the Bruns-Lakser injective hull of A in the category of meet semilattices and semilattice homomorphisms.Since every regular sigma-frame is the cozero part of a regular Lindeldof frame, this result points towards lambda-tightness. For any regular Lindeldof frame L, the normal completion of Coz L embeds in L as the sublocale generated by Coz L. Although this completion is clearly contained in every sublocale having the same cozero part as L, we show by example that its cozero part need not be the same as the cozero part as L. We prove that a sublocale S is lambda-tight in L iff S has the same cozero part as L. The aforementioned counterexample shows that the completion of Coz L is not always -tight in L; on the other hand, we present a large class of locales for which this is the case.

Czech name

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Czech description

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Type

J_imp - 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

<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

Continuities

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

Publication year

2017

Confidentiality

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

Name of the periodical

Quaestiones Mathematicae

ISSN

1607-3606

e-ISSN

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Volume of the periodical

40

Issue of the periodical within the volume

3

Country of publishing house

ZA - SOUTH AFRICA

Number of pages

16

Pages from-to

347-362

UT code for WoS article

000401713200005

EID of the result in the Scopus database

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