# Which properties are false for an empty set? [closed]

An empty set is closed, open, bounded, convex... All of that is vacuously true.

I wonder which properties are false for empty set?

## closed as too broad by Eevee Trainer, Derek Elkins, Shailesh, Lord Shark the Unknown, Lee David Chung LinMay 16 at 4:59

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• It's false that the empty set is nonempty. – Clayton May 16 at 1:37
• what other properties are you considering? – Graham Kemp May 16 at 1:37
• Any statement that starts "for all $x \in X$..." will be true if $X=\emptyset$. Any statement that starts "there exists $x \in X$..." will be false if $X=\emptyset$. – kccu May 16 at 1:39
• As an example, the empty set is not a star domain. – kccu May 16 at 1:41
• @N.S. In the definition of a topology the empty set is required to be closed and open. And it IS convex. – DanielWainfleet May 16 at 2:28