位相を用いた連続写像の定義
$(X, \mathcal{O}_X)$: a topological space$(Y, \mathcal{O}_Y)$: a topological space
$f : X \longmapsto Y$: a map
$$ f \text{ is continuous } \Longleftrightarrow {}^{\forall}O \in \mathcal{O}_Y \text{, } f^{-1}(O) \in \mathcal{O}_X $$
$(Y, \mathcal{O}_Y)$: a topological space
$f : X \longmapsto Y$: a map
$$ f \text{ is continuous } \Longleftrightarrow {}^{\forall}O \in \mathcal{O}_Y \text{, } f^{-1}(O) \in \mathcal{O}_X $$