Definition: Continuous Function

Let $(X,\mathcal O_X)$ and $(Y,\mathcal O_Y)$ be topological spaces. A function $f:X\to Y$ is continuous if the inverse image $f^{-1}(B)$ of every open set $B$ in $Y$ is open in $X$, formally $$B\in\mathcal O_Y\Rightarrow f^{-1}(B)\in\mathcal O_X.$$

Definitions: 1 2
Examples: 3
Proofs: 4 5 6 7
Propositions: 8 9 10 11

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