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Definition

In premetric spaces

Let $T$ be a type and $S$ be a set$T$ - and a$T$-premetric space. An endofunction $f:S \to S$ is continuous at a point $c:S$ if the limit of $f$ approaching $c$ exists and is equal to$f(c)$

A function $f$ is pointwise continuous if it is continuous at all points $c$:

See also

• premetric space
• limit of a function