Order summable
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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
- Ordered topological vector space
- Order topology (functional analysis) – Topology of an ordered vector space
- Ordered vector space – Vector space with a partial order
- Vector lattice – Partially ordered vector space, ordered as a lattice
References
Bibliography
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