Syndetic set

In mathematics, a syndetic set is a subset of the natural numbers having the property of "bounded gaps": that the sizes of the gaps in the sequence of natural numbers is bounded.

Definition

A set is called syndetic if for some finite subset of

where . Thus syndetic sets have "bounded gaps"; for a syndetic set , there is an integer such that for any .

See also

References

  • McLeod, Jillian (2000). "Some Notions of Size in Partial Semigroups" (PDF). Topology Proceedings. 25 (Summer 2000): 317–332.
  • Bergelson, Vitaly (2003). "Minimal Idempotents and Ergodic Ramsey Theory" (PDF). Topics in Dynamics and Ergodic Theory. London Mathematical Society Lecture Note Series. Vol. 310. Cambridge University Press, Cambridge. pp. 8–39. doi:10.1017/CBO9780511546716.004.
  • Bergelson, Vitaly; Hindman, Neil (2001). "Partition regular structures contained in large sets are abundant". Journal of Combinatorial Theory. Series A. 93 (1): 18–36. doi:10.1006/jcta.2000.3061.
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