Category:Countable Complement Topology
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This category contains results about Countable Complement Topology.
Definitions specific to this category can be found in Definitions/Countable Complement Topology.
Let $S$ be an infinite set whose cardinality is usually taken to be uncountable.
Let $\tau$ be the set of subsets of $S$ defined as:
- $H \in \tau \iff \relcomp S H$ is countable, or $H = \O$
where $\relcomp S H$ denotes the complement of $H$ relative to $S$.
In this definition, countable is used in its meaning that includes finite.
Then $\tau$ is the countable complement topology on $S$, and the topological space $T = \struct {S, \tau}$ is a countable complement space.
Subcategories
This category has only the following subcategory.
C
Pages in category "Countable Complement Topology"
The following 25 pages are in this category, out of 25 total.
C
- Compact Sets in Countable Complement Space
- Countable Complement Space is Connected
- Countable Complement Space is Irreducible
- Countable Complement Space is Lindelöf
- Countable Complement Space is Locally Connected
- Countable Complement Space is not Countably Compact
- Countable Complement Space is not Countably Metacompact
- Countable Complement Space is not First-Countable
- Countable Complement Space is not Separable
- Countable Complement Space is not Sigma-Compact
- Countable Complement Space is not T2
- Countable Complement Space is not T3, T4 or T5
- Countable Complement Space is not Weakly Countably Compact
- Countable Complement Space is Pseudocompact
- Countable Complement Space is T1
- Countable Complement Space Satisfies Countable Chain Condition
- Countable Complement Topology is Expansion of Finite Complement Topology
- Countable Complement Topology is Topology