TY - JOUR
T1 - Generalized spectra and applications to finite distributive lattices
AU - Sioen, Mark
AU - Van Den Haute, Wouter
AU - Lowen, Wendy
N1 - Funding Information:
This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 817762 ).
Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2024
Y1 - 2024
N2 - In our previous paper on frames of continuous functions, the classical adjunction between topological spaces and frames was generalized to a setup in which an arbitrary topological frame replaces the two element chain. The relevant composition of adjoints yields an endofunctor on topological spaces which in general fails to be idempotent. In this paper we prove a formula for iterations of this functor under certain conditions. We apply our result to the construction of finite free distributive lattices and Boolean algebras.
AB - In our previous paper on frames of continuous functions, the classical adjunction between topological spaces and frames was generalized to a setup in which an arbitrary topological frame replaces the two element chain. The relevant composition of adjoints yields an endofunctor on topological spaces which in general fails to be idempotent. In this paper we prove a formula for iterations of this functor under certain conditions. We apply our result to the construction of finite free distributive lattices and Boolean algebras.
UR - http://www.scopus.com/inward/record.url?scp=85181255248&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2023.107588
DO - 10.1016/j.jpaa.2023.107588
M3 - Article
VL - 6
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
M1 - 107588
ER -