of and There exists an open (in ) subset such that is a dense subset of The complement of a preopen set is called . if . The complement of a b-open set is called . or if it satisfies any of the following equivalent conditions: is a regular closed subset of There exists a preopen subset of such that The complement of a β-open set is called . if it satisfies any of the following equivalent conditions: Whenever a sequence in converges to some point of then that sequence is eventually in Explicitly, this means that if is a sequence in and if there exists some is such that in then is eventually in (that is, there exists some integer such that if then ). is equal to its in which by definition is the set The complement of a sequentially open set is called . A subset is sequentially closed in if and only if is equal to its , which by definition is the set consisting of all for which there exists a sequence in that converges to (in ). and is said to have if there exists an open subset such that is a meager subset, where denotes the symmetric difference. The subset is said to have the Baire property in the restricted sense if for every subset of the intersection has the Baire property relative to . if . The complement in of a semi-open set is called a set. The (in ) of a subset denoted by is the intersection of all semi-closed subsets of that contain as a subset. if for each there exists some semiopen subset of such that (resp. ) if its complement in is a θ-closed (resp. ) set, where by definition, a subset of is called (resp. ) if it is equal to the set of all of its θ-cluster points (resp. δ-cluster points). A point is called a (resp. a ) of a subset if for every open neighborhood of in the intersection is not empty (resp. is not empty). Using the fact that and whenever two subsets satisfy the following may be deduced: Every α-open subset is semi-open, semi-preopen, preopen, and b-open. Every b-open set is semi-preopen (i.e. β-open). Every preopen set is b-open and semi-preopen. Every semi-open set is b-open and semi-preopen. Moreover, a subset is a regular open set if and only if it is