I am interested in the name for the following notion of continuity:
Say that the function $f:\mathbb{R}^d \to \mathbb{R}$ is $(??)-$continuous at $x$ if there exists a sequence $x_n\to x$ with $x_n\neq x$ such that $f(x_{n})\to f(x)$.
For instance, I believe this rules out removable discontinuities, but allows for functions that have jump discontinuities.
Does anyone know the proper term for this notion of continuity?