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Title: Generating sublocales by subsets and relations: a tangle of adjunctions
Authors: Moshier, M. Andrew 
Picado, Jorge 
Pultr, Aleš 
Issue Date: 2017
Publisher: Springer
Project: info:eu-repo/grantAgreement/FCT/5876/147205/PT 
Serial title, monograph or event: Algebra universalis
Volume: 78
Issue: 1
Abstract: Generalizing the obvious representation of a subspace Y⊆X as a sublocale in Ω(X) by the congruence {(U,V)|U∩Y=V∩Y}, one obtains the congruence {(a,b)|o(a)∩S=o(b)∩S}, first with sublocales S of a frame L, which (as it is well known) produces back the sublocale S itself, and then with general subsets S⊆L. The relation of such S with the sublocale produced is studied (the result is not always the sublocale generated by S). Further, we discuss in general the associated adjunctions, in particular that between relations on L and subsets of L and view the aforementioned phenomena in this perspective.
Other Identifiers: 10.1007/s00012-017-0446-z
DOI: 10.1007/s00012-017-0446-z
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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