| context | $\langle X,\mathcal{T}_X\rangle$ … topological space |
| context | $\langle Y,\mathcal{T}_Y\rangle$ … topological space |
| definiendum | $ f\in \mathrm{it} $ |
| inclusion | $ f:X\to Y $ |
| for all | $V\in \mathcal{T}_Y$ |
| postulate | $ f^{-1}(V)\in\mathcal{T}_X $ |
A function to $\mathbb R^n$ is continuous iff all its components are.
clarify topologies here