c0 Space
# Definition
We define $c_0$ as $$c_{0} := {({x}{n}){n=1}^{\infty} \subset \mathbb{R} : \lim\limits_{n \in \mathbb{N}} x_{n} \to 0}$$ equipped with the norm $||x||{\infty} := \sup\limits{n \in \mathbb{N}} |x_{n}|$ for $x \in l_{\infty}$.
Search
We define $c_0$ as $$c_{0} := {({x}{n}){n=1}^{\infty} \subset \mathbb{R} : \lim\limits_{n \in \mathbb{N}} x_{n} \to 0}$$ equipped with the norm $||x||{\infty} := \sup\limits{n \in \mathbb{N}} |x_{n}|$ for $x \in l_{\infty}$.