Category:Definitions/Set Boundaries

This category contains definitions related to Set Boundaries.
Related results can be found in Category:Set Boundaries.

Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$.

Definition from Closure and Interior

The boundary of $H$ consists of all the points in the closure of $H$ which are not in the interior of $H$.

Thus, the boundary of $H$ is defined as:

$\partial H := H^- \setminus H^\circ$

where $H^-$ denotes the closure and $H^\circ$ the interior of $H$.