Why is empty set an open set?

I thought about it for a long time, but I can’t come up some good ideas. I think that empty set has no elements,how to use the definition of an open set to prove the proposition.
The definition of an open set: a set S in n-dimensional space is called open if all its points are interior points.

Answer

It’s vacuously true. All points are interior points, have a blue-eyed pet unicorn, and live in Surrey.

Attribution
Source : Link , Question Author : python3 , Answer Author : Hagen von Eitzen

Leave a Comment