Q:

Why are only the trivial subsets clopen in $\Bbb R^n$?

What topological property does $\Bbb R^n$ have which accounts for only the trivial sets ($\emptyset, \Bbb R^n$) being clopen? Is there a more general type of space where this is true? thanks

A:

By definition, this "general type" of space is connected spaces.

