Category:Dilation of Subsets of Vector Spaces
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This category contains results about Dilation of Subsets of Vector Spaces.
Definitions specific to this category can be found in Definitions/Dilation of Subsets of Vector Spaces.
Let $E$ be a subset of $X$.
Let $\lambda \in K$.
The dilation of $E$ by $\lambda$ is defined and written as:
- $\lambda E := \set {\lambda x : x \in E}$
where $\lambda x$ is the scalar product of $x$ by $\lambda$.
Subcategories
This category has the following 4 subcategories, out of 4 total.
Pages in category "Dilation of Subsets of Vector Spaces"
The following 15 pages are in this category, out of 15 total.
D
- Dilation of Closed Set in Topological Vector Space is Closed Set
- Dilation of Closure of Set in Topological Vector Space is Closure of Dilation
- Dilation of Compact Set in Topological Vector Space is Compact
- Dilation of Complement of Set in Vector Space
- Dilation of Convex Set in Vector Space is Convex
- Dilation of Interior of Set in Topological Vector Space is Interior of Dilation
- Dilation of Intersection of Subsets of Vector Space
- Dilation of Open Set in Normed Vector Space is Open
- Dilation of Subset of Vector Space Distributes over Sum
- Dilation of Union of Subsets of Vector Space
- Dilations of von Neumann-Bounded Neighborhood of Origin in Topological Vector Space form Local Basis for Origin