Let \(X\) and \(Y\) be topological spaces and \(f\colon X\to Y\) continuous . If \(Y\) is a subspace of \(Z\), then \(f\colon X\to Z\) is continuous.
Proof
The statement follows by composing \(f\) with the inclusion map \(Y\hookrightarrow Z\) (that is continuous).