This is a notation question:
If $A$ is a set in a topological space and $\bar{A}$ is its closure, is there a (standard) name for $\bar{A}\setminus A$?
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.
Sign up to join this communityThis is a notation question:
If $A$ is a set in a topological space and $\bar{A}$ is its closure, is there a (standard) name for $\bar{A}\setminus A$?
You could use "external boundary"... and "internal boundary" for A minus its interior
The english word for the common french expression used for this is "frontier".
To summarize here all the answers that people gave in comments:
1) There seems not to be a standard notation/terminology for $\bar{A}\setminus A$ in the literature.
2) Points in $\bar{A}\setminus A$ can be referred to as "limit/closure points not in $A$" or "external limit/closure points".
3) $\bar{A}\setminus A$ is different in general than the boundary/frontier of $A$ which is defined as $\bar{A}\setminus \mathrm{int}(A)$, where $\mathrm{int}(A)$ is the interior of $A$.