Hilbert Space Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HSE Home  >  Th. List  >  df-ch Structured version   Visualization version   GIF version

Definition df-ch 28990
 Description: Define the set of closed subspaces of a Hilbert space. A closed subspace is one in which the limit of every convergent sequence in the subspace belongs to the subspace. For its membership relation, see isch 28991. From Definition of [Beran] p. 107. Alternate definitions are given by isch2 28992 and isch3 29010. (Contributed by NM, 17-Aug-1999.) (New usage is discouraged.)
Assertion
Ref Expression
df-ch C = {S ∣ ( ⇝𝑣 “ (m ℕ)) ⊆ }

Detailed syntax breakdown of Definition df-ch
StepHypRef Expression
1 cch 28698 . 2 class C
2 chli 28696 . . . . 5 class 𝑣
3 vh . . . . . . 7 setvar
43cv 1530 . . . . . 6 class
5 cn 11630 . . . . . 6 class
6 cmap 8398 . . . . . 6 class m
74, 5, 6co 7148 . . . . 5 class (m ℕ)
82, 7cima 5551 . . . 4 class ( ⇝𝑣 “ (m ℕ))
98, 4wss 3934 . . 3 wff ( ⇝𝑣 “ (m ℕ)) ⊆
10 csh 28697 . . 3 class S
119, 3, 10crab 3140 . 2 class {S ∣ ( ⇝𝑣 “ (m ℕ)) ⊆ }
121, 11wceq 1531 1 wff C = {S ∣ ( ⇝𝑣 “ (m ℕ)) ⊆ }
 Colors of variables: wff setvar class This definition is referenced by:  isch  28991
 Copyright terms: Public domain W3C validator