Category:Excluded Point Topology
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This category contains results about Excluded Point Topology.
Definitions specific to this category can be found in Definitions/Excluded Point Topology.
Let $S$ be a set which is non-empty.
Let $p \in S$ be some particular point of $S$.
We define a subset $\tau_{\bar p}$ of the power set $\powerset S$ as:
- $\tau_{\bar p} = \set {A \subseteq S: p \notin A} \cup \set S$
That is, all the subsets of $S$ which do not include $p$, along with the set $S$.
Then $\tau_{\bar p}$ is a topology called the excluded point topology on $S$ by $p$, or just an excluded point topology.
Subcategories
This category has the following 10 subcategories, out of 10 total.
E
- Excluded Point Space is T0 (3 P)
- Excluded Set Topology (2 P)
S
- Sierpiński Space (9 P)
Pages in category "Excluded Point Topology"
The following 29 pages are in this category, out of 29 total.
E
- Excluded Point Space is Compact
- Excluded Point Space is Connected
- Excluded Point Space is First-Countable
- Excluded Point Space is Locally Path-Connected
- Excluded Point Space is not Arc-Connected
- Excluded Point Space is not Irreducible
- Excluded Point Space is not Locally Arc-Connected
- Excluded Point Space is not Perfectly T4
- Excluded Point Space is Path-Connected
- Excluded Point Space is Scattered
- Excluded Point Space is Sequentially Compact
- Excluded Point Space is T0
- Excluded Point Space is T5
- Excluded Point Space is Ultraconnected
- Excluded Point Topology is not T3
- Excluded Point Topology is Open Extension Topology of Discrete Topology
- Excluded Point Topology is T4
- Excluded Point Topology is Topology