Let ( L , d 1 ) {\displaystyle {}(L,d_{1})} and ( M , d 2 ) {\displaystyle {}(M,d_{2})} be metric spaces,
a mapping, and x ∈ L {\displaystyle {}x\in L} . The mapping f {\displaystyle {}f} is called continuous in x {\displaystyle {}x} if for every ϵ > 0 {\displaystyle {}\epsilon >0} there exists a δ > 0 {\displaystyle {}\delta >0} such that
holds. The mapping f {\displaystyle {}f} is called continuous if it is continuous in x {\displaystyle {}x} for every x ∈ L {\displaystyle {}x\in L} .
and 
be
metric spaces,
.
The mapping 
is called continuous in 
if for every
there exists a
such that
is called continuous if it is continuous in for every
.
