# Thread: Is the convex hull of a compact set still compact in the infinite dimensional space?

1. ## Is the convex hull of a compact set still compact in the infinite dimensional space?

I guess the convex hull of a compact set is still compact in the infinite dimensional space.
Am I right?

2. ## Re: Is the convex hull of a compact set still compact in the infinite dimensional sp

If you mean the closed convex hull you're right (if the space is complete). You have to show that the closed convex hull is precompact.