The main purpose of this paper is to introduce *-operfect, τ*-clopen, α-*-closed, strongly α-*-closed and pre-*-closed sets. We compare them and obtain a diagram to show their relationships among these sets and related
Summary New classes of sets called O-closed sets and Os-closed sets are introduced and studied. Also, we introduce and study O-continuous functions and Os-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces O-T1/2 and O-Ts.
We introduce new classes of sets called Λg-closed sets and Λg-open sets in topological spaces. We also investigate several properties of such sets. It turns out that Λg-closed sets and Λg-open sets are weaker forms of closed sets and open sets, respectively and stronger forms of g-closed sets and g-open sets, respectively.
The purpose of this paper is to introduce ideal minimal spaces and to investigate the relationships between minimal spaces
and ideal minimal spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and
characterizations related to these sets are given.
An ideal on a set X is a nonempty collection of subsets of X with heredity property which is also closed under finite unions. The concept of generalized closed sets in bitopological
spaces was introduced by Sundaram. In this paper, we introduce and study the concept of generalized closed sets with respect
to an ideal in an ideal bitopological space.