If is continuous and is a vector subspace of then is continuous.
How does one prove continuity with restricted into a set?
Let be continuous and then is continuous.
I need a hint for this one.
Can you show that the topologies have the same properties?
For example if you start with a simple region (and no holes of any kind), then the subset of any simple region is simple and the topologies are the same then continuity in the sub-space under the preservation of the topology will have the same properties of that as the non sub-space.