Phrase guide

Hausdorff gap

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

No pronunciation record was provided for this word.

1

noun

Meaning 1

A pair of collections of integer sequences such that there is no integer sequence lying between the two.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, order-theory, sciences, set-theory

Examples

  • The existence of Hausdorff gaps shows that the partially ordered set of possible growth rates of sequences is not complete.^([Wikipedia])
  • 2013, Ilijas Farah, Eric Wofsey, 3: Set theory and operator algebras, James Cummings, Ernest Schimmerling (editors), Appalachian Set Theory: 2006-2012, London Mathematical Society, Cambridge University Press, page 101, This family is one of the instances of incompactness of ω1 that are provable in ZFC, along with Hausdorff gaps, special Aronszajn trees, or nontrivial coherent families of partial functions.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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