Form Classes

Form equivalence class Howard-Rubin Number: 0

Statement:

The following are equivalent in a Hilbert  space:

  1. The closed unit  ball  is  sequentially compact.
  2. Each unconditionally convergent series converges absolutely.
  3. Each ortho-normal system is Dedekind finite.

Howard-Rubin number: 0 I

Citations (articles): Brunner [1983b] Sequential compactness and the axiom of choice

Connections (notes): Note [94] Relationships between the different definitions of finite

References (books):

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