Quasicomponents and Components are Equal in Compact Hausdorff Space

Theorem

Let $T = \left({S, \tau}\right)$ be a compact Hausdorff space.

Then for each $A \subseteq S$:

$A$ is a component of $S$ if and only if $A$ is a quasicomponent of $S$.

Proof

This theorem requires a proof. In particular: Follows from Quasicomponent of Compact Hausdorff Space is Connected 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.