Filter on Set/Examples/Closed Real Intervals

Examples of Filters on Sets

Let $\FF$ be the set of all closed real intervals $\closedint x y$ such that:

$0 < x < \dfrac 1 2 < y < 1$

Then $\FF$ is a filter on the closed real interval $\closedint 0 1$.

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.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): filter
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): filter