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