# Category:Finite Complement Topology

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This category contains results about Finite Complement Topology.

Definitions specific to this category can be found in Definitions/Finite Complement Topology.

Let $S$ be a set whose cardinality is usually specified as being infinite.

Let $\tau$ be the set of subsets of $S$ defined as:

- $H \in \tau \iff \relcomp S H \text { is finite, or } H = \O$

where $\relcomp S H$ denotes the complement of $H$ relative to $S$.

Then $\tau$ is the **finite complement topology on $S$**, and the topological space $T = \struct {S, \tau}$ is a **finite complement space**.

## Pages in category "Finite Complement Topology"

The following 27 pages are in this category, out of 27 total.

### C

- Clopen Sets in Finite Complement Topology
- Closed Set of Uncountable Finite Complement Topology is not G-Delta
- Closure of Infinite Subset of Finite Complement Space
- Countable Complement Topology is Expansion of Finite Complement Topology
- Countable Finite Complement Space is not Locally Path-Connected
- Countable Finite Complement Space is not Path-Connected

### D

### F

- F-Sigma and G-Delta Subsets of Uncountable Finite Complement Space
- Finite Complement Space is Connected
- Finite Complement Space is Irreducible
- Finite Complement Space is Locally Connected
- Finite Complement Space is not T2
- Finite Complement Space is not T3, T4 or T5
- Finite Complement Space is T1
- Finite Complement Topology is Minimal T1 Topology
- Finite Complement Topology is not Metrizable
- Finite Complement Topology is Separable
- Finite Complement Topology is Topology
- Fort Space is Excluded Point Space with Finite Complement Space