Abstract
Joins in the frame of nuclei are hard to describe explicitly because a pointwise join of a set of closure operators on a complete lattice fails to be idempotent in general. We calculate joins of nuclei as least fixed points of inflationary operators on prenuclei. Using a recent fixed-point theorem due to Pataraia, we deduce an induction principle for joins of nuclei. As an illustration of the technique, we offer a simple (and also intuitionistic) proof of the localic Hofmann-Mislove Theorem.
| Original language | English |
|---|---|
| Pages (from-to) | 117-124 |
| Number of pages | 8 |
| Journal | Applied Categorical Structures |
| Volume | 11 |
| Issue number | 2 |
| Publication status | Published - 1 Jan 2003 |