On some properties of Noetherian topological spaces
by
Ivan Gotchev
Central Connecticut State University
Coauthors: Hristo Mintchev (University of Forestry, Sofia, Bulgaria)

A topological space X is called Noetherian if every nonempty set of closed subsets of X ordered by inclusion has a minimal element.

It is well-known that every Noetherian topological space is compact and that every subspace of a Noetherian topological space is Noetherian.

We will discuss some other properties of the Notherian topological spaces. We will show for example, that every Notherian topological space X is sequentially compact and that the sequential topology on X inherits the Notherian property. Examples of Noetherian topological spaces will be given which are not sequential spaces. Necessary and sufficient conditions for a Noetherian topological space to be sequential will be discussed.

Date received: February 27, 2003