Category:Compact Complement Topology
Jump to navigation
Jump to search
This category contains results about Compact Complement Topology.
Let $T = \struct {\R, \tau}$ be the real number line with the usual (Euclidean) topology.
Let $\tau^*$ be the set defined as:
- $\tau^* = \leftset {S \subseteq \R: S = \O \text { or } \relcomp \R S}$ is compact in $\rightset {\struct {\R, \tau} }$
where $\relcomp \R S$ denotes the complement of $S$ in $\R$.
Then $\tau^*$ is the compact complement topology on $\R$, and $T^* = \struct {\R, \tau^*}$ is the compact complement space on $\R$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Compact Complement Topology"
The following 15 pages are in this category, out of 15 total.
C
- Compact Complement Space is not T2, T3, T4 or T5
- Compact Complement Topology is Coarser than Euclidean Topology
- Compact Complement Topology is Compact
- Compact Complement Topology is Connected
- Compact Complement Topology is First-Countable
- Compact Complement Topology is Irreducible
- Compact Complement Topology is Locally Connected
- Compact Complement Topology is not Ultraconnected
- Compact Complement Topology is Second-Countable
- Compact Complement Topology is Separable
- Compact Complement Topology is Sequentially Compact
- Compact Complement Topology is T1
- Compact Complement Topology is Topology
- Countable Local Basis in Compact Complement Topology