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A regular closed set is subset of a topological space which is the closure of an open set. In other words, it is the closure of its own interior. Regular closed sets are also called canonical closed. Every closed set contains a maximal regular closed set, namely the closure of its interior. The union of two regular closed sets is a regular closed set, but their intersection need not be. A set which is a finite intersection of regular closed sets is called a π-set.

The collection of regular closed sets forms a Boolean algebra under the following operations:,  , and. The same can be done for the collection of regular open sets.

A set which is the interior of a closed set is called a regular open set (also called canonical open). In other words, it is a set which is the interior of its own closure. Every open set is contained in a smallest regular open set, namely the interior of its closure. Regular open sets can also be defined as complements of regular closed canonical sets, and vice versa.