Skip to the content

Math 2.0

General topology Standard examples of topologies Example

Cofinite topology

Example

Let $X$ be a set and let $\tau$ consist of $\varnothing$ and of all sets $U \subseteq X$ whose complement $X \setminus U$ is finite. Then $\tau$ is a topology on $X$ , the cofinite topology.

Remarks

The closed sets are $X$ and the finite subsets of $X$ . The cofinite topology is T1: each one-point set is closed. If $X$ is infinite, any two nonempty open sets meet. Thus the space is not Hausdorff. Each space with the cofinite topology is compact.

Further reading

Web https://en.wikipedia.org/wiki/Cofiniteness, Cofinite topology

About this page

Tag	`0B906ZBTMZ`
URI	`m2://0B906ZBTMZ`
Aliases	`finite-complement-topology`
Kind	example
Writing	W2 usable
MSC	54A05
Instance of	Topological space

Markdown · JSON · Edit on GitHub

What this page needs for W3

a person confirmed each agent-written section: rule P04 (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.