Every open set in a metric space is also a closed set.
10pts
In topology, a continuous function between topological spaces preserves the connectedness of sets.
10pts
The product topology on a product of topological spaces is always the coarsest topology that makes all the projection maps continuous.
10pts
A compact space is always connected.
10pts
Every homeomorphism is a continuous bijection with a continuous inverse.
10pts
In a Hausdorff space, any two distinct points can be separated by disjoint open sets.
10pts