Let be the rational numbers, and let be a closed interval in . An function is continuous at a point if the limit of approaching exists and is equal to
is pointwise continuous in if it is continuous at all points :
In premetric spaces
Let and be types, be a -premetric space and be a -premetric space. An function is continuous at a point if the limit of approaching exists and is equal to
is pointwise continuous if it is continuous at all points :