##  [Schauder Basis](/schauder-basis) 

  ##  [Schauder Basis](https://puremath.quantumdictionary.io/schauder-basis-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A sequence (x_n) in a topological vector space such that every element of the space admits a unique representation as a (topologically) convergent infinite series x = ∑_{n=1}^∞ a_n x_n of scalars, where convergence is with respect to the space's topology.