Hausdorff gap

Etymology
Named after German mathematician (1868–1942), who published proof of the first example in 1909.

Noun

 * 1)  A pair of collections of integer sequences such that there is no integer sequence lying between the two.
 * 2) * 2013, Ilijas Farah, Eric Wofsey, 3: Set theory and operator algebras, James Cummings, Ernest Schimmerling (editors), Appalachian Set Theory: 2006-2012,, , page 101,
 * This family is one of the instances of incompactness of $$\omega_1$$ that are provable in ZFC, along with Hausdorff gaps, special Aronszajn trees, or nontrivial coherent families of partial functions.
 * 1) * 2013, Ilijas Farah, Eric Wofsey, 3: Set theory and operator algebras, James Cummings, Ernest Schimmerling (editors), Appalachian Set Theory: 2006-2012,, , page 101,
 * This family is one of the instances of incompactness of $$\omega_1$$ that are provable in ZFC, along with Hausdorff gaps, special Aronszajn trees, or nontrivial coherent families of partial functions.
 * This family is one of the instances of incompactness of $$\omega_1$$ that are provable in ZFC, along with Hausdorff gaps, special Aronszajn trees, or nontrivial coherent families of partial functions.

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