Solution
= Solution
The extended-real functional $f:X\to\overline{\mathbb R}$ is <sequentially lower semicontinuous> in the topology $\tau_X$ when every sequence $x_n\to x$ in $\tau_X$ satisfies
$$
f(x)\leq\liminf_{n\to\infty}f(x_n).
$$
= Solution
The extended-real functional $f:X\to\overline{\mathbb R}$ is <sequentially lower semicontinuous> in the topology $\tau_X$ when every sequence $x_n\to x$ in $\tau_X$ satisfies
$$
f(x)\leq\liminf_{n\to\infty}f(x_n).
$$