may 2022 Uniformities and a quantale structure on localic groups
Jorge Picado, Aleš Pultr
Bull. Belg. Math. Soc. Simon Stevin 28(4): 561-578 (may 2022). DOI: 10.36045/j.bbms.210823


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.


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Jorge Picado. Aleš Pultr. "Uniformities and a quantale structure on localic groups." Bull. Belg. Math. Soc. Simon Stevin 28 (4) 561 - 578, may 2022.


Published: may 2022
First available in Project Euclid: 11 May 2022

Digital Object Identifier: 10.36045/j.bbms.210823

Primary: 06D22 , 06F07 , 18F70 , 54H11

Keywords: frame , frame entourage , involutive quantale , locale , localic group , localic group uniformities , ordered semigroup , Quantale

Rights: Copyright © 2022 The Belgian Mathematical Society


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Vol.28 • No. 4 • may 2022
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