# Category:Space of Bounded Sequences

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This category contains results about **Space of Bounded Sequences**.

Definitions specific to this category can be found in **Definitions/Space of Bounded Sequences**.

Let $\mathbb F \in \set {\R, \C}$.

We define the **space of bounded sequences** on $\mathbb F$, written $\map {\ell^\infty} {\mathbb F}$, by:

\(\ds \map {\ell^\infty} {\mathbb F}\) | \(=\) | \(\ds \set {\sequence {x_n}_{n \mathop \in \N} \in {\mathbb F}^\N : \sequence {x_n}_{n \mathop \in \N} \text { is a bounded sequence} }\) | ||||||||||||

\(\ds \) | \(=\) | \(\ds \set {\sequence {x_n}_{n \mathop \in \N} \in {\mathbb F}^\N : \sup_{n \mathop \in \N} \cmod {x_n} < \infty}\) |

where ${\mathbb F}^\N$ is the space of all $\mathbb F$-valued sequences.

## Pages in category "Space of Bounded Sequences"

The following 2 pages are in this category, out of 2 total.