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c0 Space

Last updated Nov 1, 2022

# 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 $x \in l_{\infty}$.

# Remarks

  1. c0 is Banach