Category:Definitions/Isolated Points
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This category contains definitions related to Isolated Points in the context of Topology.
Related results can be found in Category:Isolated Points.
Let $T = \struct {S, \tau}$ be a topological space.
Isolated Point of Subset
$x \in H$ is an isolated point of $H$ if and only if:
- $\exists U \in \tau: U \cap H = \set x$
That is, if and only if there exists an open set of $T$ containing no points of $H$ other than $x$.
Isolated Point of Space
When $H = S$ the definition applies to the entire topological space $T = \struct {S, \tau}$:
$x \in S$ is an isolated point of $T$ if and only if:
- $\exists U \in \tau: U = \set x$
That is, if and only if there exists an open set of $T$ containing no points of $S$ other than $x$.
Pages in category "Definitions/Isolated Points"
The following 9 pages are in this category, out of 9 total.
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- Definition:Isolated Point
- Definition:Isolated Point (Topology)
- Definition:Isolated Point (Topology)/Space
- Definition:Isolated Point (Topology)/Subset
- Definition:Isolated Point (Topology)/Subset/Definition 1
- Definition:Isolated Point (Topology)/Subset/Definition 2
- Definition:Isolated Point of Metric Space
- Definition:Isolated Point of Subset
- Definition:Isolated Point of Topological Space