Frequently closed sets are subsets of a partially ordered set that maintain a certain degree of closure under the operation of taking directed suprema. Specifically, a subset is frequently closed if, whenever a directed set has its supremum within the subset, all elements of that directed set must also be within the subset. This concept connects closely with Galois connections, where it provides a way to understand how certain structures behave under mappings and adjunctions.
congrats on reading the definition of frequently closed sets. now let's actually learn it.