Topological Closure is Closure Operator

Theorem

The topological closure operator is a closure operator.


Proof

Extensive

Follows from Set is Subset of its Topological Closure.

Increasing

Follows immediately from Topological Closure of Subset is Subset of Topological Closure.

Idempotent

Follows immediately from Closure of Topological Closure equals Closure.


This article needs to be linked to other articles.
In particular: the three concepts in the headers (link in the text)
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links.
To discuss this page in more detail, feel free to use the talk page.
When this work has been completed, you may remove this instance of {{MissingLinks}} from the code.


$\blacksquare$

This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.