Definition of "with dense range"

Question

it is written "T is a continuous map with dense range". What is the definition of map with dense range? Maybe it's simple but I am not native English speaker, thanks.

Answer 1

If $T$ is a continuous map from a topological space $X$ to a topological space $Y$, then $T$ is said to have a dense range if the set $T(X)$ is a dense subset of $Y$. That is, every non-empty open set in $Y$ has a non-empty intersection with $T(X)$.