Left-Continuous
# Definition
A Function $f: \mathbb{R} \to M$ for Metric Space at $(M, d)$ is Left-Continuous at $x \in \mathbb{R}$ if its Left Function Limit exists and, $$\lim_{y \uparrow x} f(y) = f(x)$$ We call $f$ Left-Continuous if it is Left-Continuous for all $x \in \mathbb{R}$.