maximal

定義

Here we define the maximality of covers of topological spaces.
Let X be a topological space, R be a subset family in X which is closed under finite unions. Let M be the collection of all covers by the elements in R which have no finite subcovers. A maximal R-cover means the maximal element in M wrt. the set inclusion.
For example, if R is the family of cozero sets (open sets), we have a maximal cozero (open) cover.