## Continuous function

### Set

 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 $f^{-1}(V)\in\mathcal{T}_X$

### Discussion

#### Theorems

A function to $\mathbb R^n$ is continuous iff all its components are.

clarify topologies here