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:

$H \in \tau \iff \complement_S \left({H}\right)$ is countable, or $H = \varnothing$

where $\complement_S \left({H}\right)$ 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 $T = \left({S, \tau}\right)$ is a countable complement space.