Subspace topology as initial topology for the inclusion

Let \((X, \mathcal{T})\) be a topological space, \(Y \subseteq X\) a subset. Then the subspace topology is precisely the Initialtopologie for the inclusion map \(\iota: Y \rightarrowtail X\)

corollary of:

• Basis einer Initialtopologie

and the definition of a subspace topology