# Category:Convergent Mappings

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This category contains results about **Convergent Mappings**.

Definitions specific to this category can be found in **Definitions/Convergent Mappings**.

Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.

Let $c$ be a limit point of $M_1$.

Let $f: A_1 \to A_2$ be a mapping from $A_1$ to $A_2$ defined everywhere on $A_1$ *except possibly* at $c$.

Let $\map f x$ tend to the limit $L$ as $x$ tends to $c$.

Then $f$ **converges to the limit $L$ as $x$ tends to $c$**.

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