nullhomotopic

Let \((X,\mathcal{T}_X)\) and \((Y,\mathcal{T}_Y)\) be topological spaces and \(f: X \rightarrow Y\) a map. Then \(f\) is said to be nullhomotopic, if \(f\) is homotopic relative to a constant map \(f: X \rightarrow \{y\}\)