In mathematics, specifically in order theory and functional analysis, a sequence of positive elements in a preordered vector space (that is, for all ) is called order summable if exists in .[1] For any , we say that a sequence of positive elements of is of type if there exists some and some sequence in such that for all .[1]

The notion of order summable sequences is related to the completeness of the order topology.

See also

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References

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  1. ^ a b Schaefer & Wolff 1999, pp. 230–234.

Bibliography

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  • Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
  • Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.