Metric Space Relations

We present here inclusion relations between different spaces. An arrow $A\to B$ means that all spaces of type $A$ are also of type $B$, i.e. $A$ is included in $B$.

stateDiagram
Ba: Banach Space
E: Euclidean Space
F: Fock Space
Hi: Hilbert Space
Ho: Holder Space
IP: Inner Product Space
Lp: Lp Space
L2: L2 Space
Me: Metric Space
Mi: Minkowski Space
Nv: Normed Vector Space
Q: Quantum Hilbert Space
Sc: Schwartz Space
So: Sobolev Space
SS: Sobolev-Slobodeckij Space
P: Polish Space
Pe: Pseudo-Euclidean Space
V: Vector Space

P --> Me

Ba --> V
So --> V

Nv --> Me
Nv --> V

Lp --> Nv
IP --> Nv

Hi --> Ba
Hi --> IP

F --> Hi
Ho --> Hi
Pe --> Hi
Q --> Hi
L2 --> Hi

L2 --> Lp

E --> Pe
Mi --> Pe

Sc --> So
SS --> So

The above includes different spaces:

1. Banach Space
2. Euclidean Space
3. Fock Space
4. Hilbert Space
5. Holder Space
6. Inner Product Space
7. Metric space
8. Schwarz space
9. Sobolev Space
10. Vector Space
11. Quantum Hilbert Space