Almost, Weakly and Nearly Lindel¨of Ideal Topological Spaces

The concepts of almost, weakly and nearly Lindelöf closed ideal topological spaces are introduced in this work. We examine their subspaces and the connection between the subspaces and their topological characteristics and explaine how countable covers affect Almost Lindelöf spaces and concentrate on the significance of these covers. These covers are made up of countable subfamilies whose closures cover the ideal spaces. Definitions, claims, characterizations, and observations pertaining to the recently presented concepts of almost and weakly Lindelöf ideal topological spaces are started, examined, and discussed. Additionally, the connections among various ideal topological spaces are analyzed and explored. We provide examples of the consequences of these novel ideal spaces.