What is Symmetrically continuous function?

In mathematics, a function f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } is symmetrically continuous at a point x if

The usual definition of continuity implies symmetric continuity, but the converse is not true. For example, the function x − 2 {\displaystyle x^{-2}} is symmetrically continuous at x = 0 {\displaystyle x=0} , but not continuous.

Also, symmetric differentiability implies symmetric continuity, but the converse is not true just like usual continuity does not imply differentiability.