what does superscript zero in set notation?

Question

In How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?

what does the superscripted little-bitty zero (looks like the number of degrees for temperature) mean?

Answer 1

$A^o$ is the interior of A. It's written with a small o.

The overline for closure and the superscript o for interior is inferior two dimensional notion. For example, $\overline {{\overline {A^o}}^o} = \overline {A^o}$.

Some mathematicians use $A^{o-o-} = A^{o-}$.

Answer 2

The interior $A^o\subset A$.

Incidentally, it is the largest open set contained in $A$; or the union of all open sets contained in $A$.