Find a example in $L^2$, nonempty closed but contains no element of smallest norm.
138720
Minimum principle in Hilbert space
86724
Example of a non-zero module that has no associated primes
94231
Prove that a non-empty closed convex $S$ has an extreme point iff it does not contain any line
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
1475
In an incomplete inner product space, is a closed linear subspace equal to the orthogonal complement of its orthogonal complement?
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
32819
Looking for examples of first countable, compact spaces which is not separable
116806
Find the weak sequential closure of a set in $L^2(-\pi,\pi)$
78188
How can I get the smallest possible answer with the Chinese Remainder Theorem?
43053
$L^2$ function with compact support is in $L^1$?
116112
Examples of 'almost' vector spaces where unitary law fails
63529
How to show that this set is compact in $\ell^2$
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
74498
Smallest dense subset of $\mathbb{R}$
60004
Why is $\omega$ the smallest $\infty$?
47975
Closed cone in the euclidean space $\mathbb{R}^n$
5323
Example to show the distance between two closed sets can be 0 even if the two sets are disjoint