Generalized spectra and applications to finite distributive lattices

Mark Sioen; Wouter Van Den Haute; Wendy Lowen

doi:10.1016/j.jpaa.2023.107588

Generalized spectra and applications to finite distributive lattices

Mark Sioen, Wouter Van Den Haute, Wendy Lowen

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	107588
Number of pages <span style="color:red"p> <font size="1.5"> ✽ </span> </font>	8
Journal	Journal of Pure and Applied Algebra
Volume	6
DOIs	https://doi.org/10.1016/j.jpaa.2023.107588
Publication status	Published - 2024

Bibliographical note

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.

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10.1016/j.jpaa.2023.107588

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Generalized spectra and applications to finite distributive lattices

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