# Category:Normed Vector Spaces

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This category contains results about Normed Vector Spaces.

Definitions specific to this category can be found in Definitions/Normed Vector Spaces.

Let $\struct {K, +, \circ}$ be a normed division ring.

Let $V$ be a vector space over $K$.

Let $\norm {\,\cdot\,}$ be a norm on $V$.

Then $\struct {V, \norm {\,\cdot\,} }$ is a **normed vector space**.

## Subcategories

This category has the following 6 subcategories, out of 6 total.

## Pages in category "Normed Vector Spaces"

The following 26 pages are in this category, out of 26 total.

### C

- Cauchy Sequence is Bounded/Normed Vector Space
- Characteristics of Birkhoff-James Orthogonality
- Closed and Bounded Subset of Normed Vector Space is not necessarily Compact
- Closed Ball is Closed/Normed Vector Space
- Compact Subset of Normed Vector Space is Closed and Bounded
- Composite of Continuous Mappings between Normed Vector Spaces is Continuous
- Convergent Sequence in Normed Vector Space has Unique Limit

### N

### S

- Set Closure is Smallest Closed Set/Normed Vector Space
- Space of Almost-Zero Sequences is Everywhere Dense in 2-Sequence Space
- Subset of Normed Vector Space is Everywhere Dense iff Closure is Normed Vector Space
- Subset of Normed Vector Space is Everywhere Dense iff Closure is Normed Vector Space/Necessary Condition
- Subset of Normed Vector Space is Everywhere Dense iff Closure is Normed Vector Space/Sufficient Condition
- Subspace of Normed Vector Space with Induced Norm forms Normed Vector Space