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Definition df-ch 29156
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 29157. From Definition of [Beran] p. 107. Alternate definitions are given by isch2 29158 and isch3 29176. (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 28864 . 2 class C
2 chli 28862 . . . . 5 class 𝑣
3 vh . . . . . . 7 setvar
43cv 1541 . . . . . 6 class
5 cn 11716 . . . . . 6 class
6 cmap 8437 . . . . . 6 class m
74, 5, 6co 7170 . . . . 5 class (m ℕ)
82, 7cima 5528 . . . 4 class ( ⇝𝑣 “ (m ℕ))
98, 4wss 3843 . . 3 wff ( ⇝𝑣 “ (m ℕ)) ⊆
10 csh 28863 . . 3 class S
119, 3, 10crab 3057 . 2 class {S ∣ ( ⇝𝑣 “ (m ℕ)) ⊆ }
121, 11wceq 1542 1 wff C = {S ∣ ( ⇝𝑣 “ (m ℕ)) ⊆ }
Colors of variables: wff setvar class
This definition is referenced by:  isch  29157
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