# Tag Info

## Hot answers tagged functional-analysis

### I am missing some point about Cantor's Theorem

You are forgetting the fact that $f$ is surjective onto the power set of $A$. If $A$ is a singleton then power set of $A$ is not a sigleton. It contains the empty set also. Existence of $\xi$ in the ...
• 2,176
1 vote
Accepted

### Equality with metric in metric spaces

You first part of the $\impliedby$ proof has a mistake. You write "suppose $x < y$" but you should have written "suppose $x \ne y$". You've also been a little slopping elsewhere,...
• 88.2k
1 vote
Accepted

• 61
1 vote

### Hilbert space H is separable if and only if the dual space H* is separable

The Riesz representation theorem implements a conjugate-linear isometry $$\Phi: H \to H^*: \xi \mapsto \langle \xi\mid -\rangle$$(assuming that inner product is linear in the second factor). In ...
• 19.9k

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