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Definition

In premetric spaces

Let $T$ be a type and$\mathrm{<span><del\; class="diffmod">\; S</del><ins\; class="diffmod">\; V</ins></span>}$ S V be a types,$\mathrm{<span><del\; class="diffmod">\; T</del><ins\; class="diffmod">\; S</ins></span>}$ T S - be a$T$-premetric space . An and endofunction$\mathrm{<span><del\; class="diffmod">\; f</del><ins\; class="diffmod">\; U</ins></span>}:S\to S$ f:S U \to S is be a$V$-premetric space. An function $f:S \to U$ 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