Commit 2025-04-06 21:39 8ea8a7fb

feat(PrimeSpectrum): Clopens in spectra of CommSemirings (#20533) We show that clopens in a commutative semiring are in 1-1 correspondence with pairs of elements (e,f) such that e * f = 0 and e + f = 1. This happens precisely when ![e,f] is a complete orthogonal family of idempotents. Not all idempotents in a comm. semiring has such a complement: for example, in the semiring {0, 0.5, 1} with sup as + and inf as *, 0.5 doesn't have a complement.