Closed and compact

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

Closed and compact

#1

Post by Papapetros Vaggelis »

Let \(\displaystyle{X}\) be a topological vector space, \(\displaystyle{K\subseteq X}\) a compact

subset of \(\displaystyle{X}\) and \(\displaystyle{C\subseteq X}\) a closed subset of \(\displaystyle{X}\)

such that \(\displaystyle{K\cap C=\varnothing}\).

Then, there exists an open region \(\displaystyle{V}\) of \(\displaystyle{0\in X}\) such that

\(\displaystyle{(K+V)\cap (C+V)=\varnothing}\)
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 17 guests