In mathematics, a Noetherian topological space, named for Emmy Noether, is a topological space in which closed subsets satisfy the descending chain condition...

Noetherian. Noetherian relation, a binary relation that satisfies the ascending chain condition on its elements. Noetherian topological space, a topological space...

agree in a metric space, but may not be equivalent in other topological spaces. One such generalization is that a topological space is sequentially compact...

scheme is a Noetherian topological space. But the converse is false in general; consider, for example, the spectrum of a non-Noetherian valuation ring. The...

mathematical field of topology, a hyperconnected space or irreducible space is a topological space X that cannot be written as the union of two proper...

(quasi)compact, and if the ring in question is Noetherian then the space is a Noetherian topological space. However, these facts are counterintuitive: we...

locally Noetherian, but there are important constructions that lead to more general schemes. In any (not necessarily noetherian) topological space, every...

space is a topological space whose topology can be completely characterized by its convergent/divergent sequences. They can be thought of as spaces that...

projective limits. One of the way to fix this is to consider Noetherian topological spaces; every open sets are compact so that the cokernel is a sheaf...

Noetherian ring a Noetherian topological space. The chain condition often is "inherited" by sub-objects. For example, all subspaces of a Noetherian space...