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Definition df-ch 27251
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 27252. From Definition of [Beran] p. 107. Alternate definitions are given by isch2 27253 and isch3 27271. (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 26959 . 2 class C
2 chli 26957 . . . . 5 class 𝑣
3 vh . . . . . . 7 setvar
43cv 1473 . . . . . 6 class
5 cn 10774 . . . . . 6 class
6 cmap 7619 . . . . . 6 class 𝑚
74, 5, 6co 6425 . . . . 5 class (𝑚 ℕ)
82, 7cima 4935 . . . 4 class ( ⇝𝑣 “ (𝑚 ℕ))
98, 4wss 3444 . . 3 wff ( ⇝𝑣 “ (𝑚 ℕ)) ⊆
10 csh 26958 . . 3 class S
119, 3, 10crab 2804 . 2 class {S ∣ ( ⇝𝑣 “ (𝑚 ℕ)) ⊆ }
121, 11wceq 1474 1 wff C = {S ∣ ( ⇝𝑣 “ (𝑚 ℕ)) ⊆ }
Colors of variables: wff setvar class
This definition is referenced by:  isch  27252
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