A Proposition

Algebraic Geometry
Post Reply
Papapetros Vaggelis
Community Team
Posts: 426
Joined: Mon Nov 09, 2015 1:52 pm

A Proposition

#1

Post by Papapetros Vaggelis »

Let \(\displaystyle{V}\) be an algebraic subset of \(\displaystyle{\mathbb{A}^n}\).

1. The points of \(\displaystyle{V}\) are closed for the \(\displaystyle{\rm{Zariski}}\) - topology.

2. Every ascending chain \(\displaystyle{\left(U_n\right)_{n\in\mathbb{N}}}\) of open subsets

of \(\displaystyle{V}\) eventually becomes constant. Equivalently, every descending chain of closed

subsets of \(\displaystyle{V}\) eventually becomes constant.

3. Every open covering of \(\displaystyle{V}\) has a finite subcovering.
Post Reply

Create an account or sign in to join the discussion

You need to be a member in order to post a reply

Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute

Register

Sign in

Who is online

Users browsing this forum: No registered users and 3 guests