# compactness

• October 25th 2009, 10:54 PM
compactness
What are the examples of open sets that are compact?

Is the entire space X compact?
• October 26th 2009, 11:26 AM
aliceinwonderland
Quote:

Another example is that every open set is compact in the finite complement topology on $\mathbb{Re}$.
Meanwhile, if you give a usual topology on $\mathbb{Re}$, then an open compact set is an empty set only.
If you give a subspace topology on A with respect to the usual topology on $\mathbb{Re}$, where A is a finite subset of $\mathbb{Re}$, then every open set in the topological space A is compact.