In the context of mathematics, particularly in functional analysis and topology, a **sequence space** is a type of vector space formed by sequences of elements from a given set, typically a field like the real numbers or complex numbers. A sequence space can be defined with various structures and properties, such as norms or topologies, depending on how the sequences are used or the context in which they are applied.
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A sequence space is a vector space of scalar sequences, closed under coordinatewise addition and scalar multiplication. Examples include the l-p sequence space, the l-infinity sequence space and spaces of convergent sequences.