Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with topological-vector-spaces
Search options not deleted
user 5903
A topological vector space is a vector space $V$ over a topological field $\mathbb{K}$ (typically $\mathbb{K}=\mathbb{R}$ or $\mathbb{K}=\mathbb{C}$), together with a topology on $V$ such that vector addition and scalar multiplication are both continuous. Hilbert spaces and Banach spaces are examples of topological vector spaces.
1
vote
Topology on the set of linear subspaces
Denote the intersection of a closed linear subspace $A$ with the unit sphere by $S_A$, say. You can define the distance of $A$ and $B$ to be the Hausdorff distance between $S_A$ and $S_B$. This will g …
- 11.4k
7
votes
Accepted
On the equality $\{f\in C(X), f|_A=0\}+\{f\in C(X), f|_B=0\}=\{f\in C(X), f|_{A\cap B}=0\}$
This characterizes normality.
That it implies normality was observed above by Remy.
Conversely, assume $f$ vanishes on $A\cap B$. Define $h:A\cup B\to\mathbb{R}$ by $h(x)=f(x)$ if $x\in A$ and $h(x)=0 …
- 11.4k