Sierpiński's Theorem
Jump to navigation
Jump to search
This article needs to be linked to other articles. In particular: Closed cover 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. |
Theorem
Let $\left({S, \tau}\right)$ be a compact connected Hausdorff space.
Let $\left\{{F_n: n \in \N}\right\}$ be a pairwise disjoint closed cover of $S$.
This article, or a section of it, needs explaining. In particular: In context it's obvious, but worth mentioning that $F_n$ is a finite cover as well? You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. 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 {{Explain}} from the code. |
Then $F_n = S$ for some $n \in \N$.
Proof
This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. 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 {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Source of Name
This entry was named for Wacław Franciszek Sierpiński.