Noetherian Topological Spaces
Posted: Sat Dec 19, 2015 10:53 am
- Let \( X \) be a Noetherian topological space. Show that every subspace of \( X \) is also Noetherian and that \( X \) quasi-compact.
- Let \( X \) be a topological space. Show that the following are equivalent:
- \( X \) is Noetherian.
- Every open subspace of \( Χ \) is quasi-compact.
- Every subspace of \( Χ \) is quasi-compact.
Note: "Quasi-compact" means that every open cover of \( X \) has a finite subcover.