From ProofWiki
Jump to navigation Jump to search

This category contains results about Boundaries in the context of Topology.

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$.

Then 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 $H$.