Category:Examples of Set Boundaries
Jump to navigation
Jump to search
This category contains examples of Set Boundaries in the context of Topology.
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 $H$.
Pages in category "Examples of Set Boundaries"
The following 6 pages are in this category, out of 6 total.
B
- Boundary (Topology)/Examples
- Boundary (Topology)/Examples/Half-Open Real Interval
- Boundary (Topology)/Examples/Integers in Real Numbers
- Boundary (Topology)/Examples/Open Unit Interval
- Boundary (Topology)/Examples/Rationals in Closed Unit Interval
- Boundary (Topology)/Examples/Reciprocals in Real Numbers