Category:Definitions/Topological Vector Spaces
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This category contains definitions related to Topological Vector Spaces.
Related results can be found in Category:Topological Vector Spaces.
Let $\struct {K, +_K, \circ_K, \tau_K}$ be a topological field.
Let $\struct {X, +_X, \circ_X, \tau_X}$ be a vector space over $K$.
Let $\tau_X \times \tau_X$ be the product topology of $\tau_X$ and $\tau_X$.
Let $\tau_K \times \tau_X$ be the product topology of $\tau_K$ and $\tau_X$.
We say that $\struct {X, \tau_X}$ is called a topological vector space if and only if:
| \((1)\) | $:$ | $+_X: \struct {X \times X, \tau_X \times \tau_X} \to \struct {X, \tau_X}$ is continuous | |||||||
| \((2)\) | $:$ | $\circ_X : \struct {K \times X, \tau_K \times \tau_X} \to \struct {X, \tau_X}$ is continuous |
Subcategories
This category has the following 7 subcategories, out of 7 total.
B
- Definitions/Barrelled Spaces (1 P)
Pages in category "Definitions/Topological Vector Spaces"
The following 21 pages are in this category, out of 21 total.