Word.ws English Dictionary

Hausdorff gap

Hausdorff gap noun: a pair of collections of integer sequences such that there is no integer sequence lying between the two.

Noun

Hausdorff gap (plural Hausdorff gaps)

  1. A pair of collections of integer sequences such that there is no integer sequence lying between the two.
    • The existence of Hausdorff gaps shows that the partially ordered set of possible growth rates of sequences is not complete.^([Wikipedia])
    • Of course, Hausdorff did not talk of models of set theory or prove absoluteness results. He gave a direct construction in ZFC of what is now called a Hausdorff gap and proved properties 1 through 4 for his construction. The notion of a Hausdorff gap and the proof that Hausdorff gaps are...1995, Robert M. Solovay, “*1970 [Godel's ontological proof]”, in Kurt Gödel, edited by Solomon Feferman, John W. Dawson Jr., Warren Goldfarb, Charles Parsons, and Robert M. Solovay, Kurt Gödel...

Examples of Hausdorff gap in a sentence

  • He gave a direct construction in ZFC of what is now called a Hausdorff gap and proved properties 1 through 4 for his construction.1995, Robert M. Solovay, “*1970 [Godel's ontological proof]”, in Kurt Gödel, edited by Solomon Feferman, John W. Dawson Jr., Warren...
  • Let #92;langle#92;langlea#95;#92;epsilon#58;#92;epsilonlt;#92;omega#95;1#92;rangle#92;langleb#95;#92;epsilon#58;#92;epsilonlt;#92;omega#95;1#92;rangle#92;rangle be a Hausdorff gap.1997, Winfried Just, Martin Weese, Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician, American Mathematical...

Forms of Hausdorff gap

pluralHausdorff gaps

Origin of Hausdorff gap

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

Questions about Hausdorff gap

What does Hausdorff gap mean?
Hausdorff gap means a pair of collections of integer sequences such that there is no integer sequence lying between the two.
How do you use Hausdorff gap in a sentence?
He gave a direct construction in ZFC of what is now called a Hausdorff gap and proved properties 1 through 4 for his construction.
What part of speech is Hausdorff gap?
Hausdorff gap is a noun.
What is the plural of Hausdorff gap?
The plural of Hausdorff gap is Hausdorff gaps.

Words near Hausdorff gap in the dictionary

  1. Hausdorff contents
  2. Hausdorff dimension
  3. Hausdorff dimensions
  4. Hausdorff distance
  5. Hausdorff distances
  6. Hausdorff gap
  7. Hausdorff gaps
  8. Hausdorff metric
  9. Hausdorff metrics
  10. Hausdorff space
  11. Hausdorff spaces

Source and license

Adapted from Wiktionary: Hausdorff gap (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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