Exact and Strongly Exact Filters

Authors

M. A. Moshier, Chapman UniversityFollow
A. Pultr, Charles University, PragueFollow
A. L. Suarez, University of BirminghamFollow

Document Type

Article

Publication Date

7-25-2020

Abstract

A meet in a frame is exact if it join-distributes with every element, it is strongly exact if it is preserved by every frame homomorphism. Hence, finite meets are (strongly) exact which leads to the concept of an exact resp. strongly exact filter, a filter closed under exact resp. strongly exact meets. It is known that the exact filters constitute a frame FiltE(L) somewhat surprisingly isomorphic to the frame of joins of closed sublocales. In this paper we present a characteristic of the coframe of meets of open sublocales as the dual to the frame of strongly exact filters FiltsE(L).

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Applied Categorical Structures in 2020 following peer review. The final publication may differ and is available at Springer via https://doi.org/10.1007/s10485-020-09602-0.

A free-to-read copy of the final published article is available here.

Recommended Citation

Moshier, M.A., Pultr, A. & Suarez, A.L. Exact and Strongly Exact Filters. Appl Categor Struct (2020). https://doi.org/10.1007/s10485-020-09602-0

Peer Reviewed

1

Copyright

Springer