Function space

Function algebra

Let 𝕂 be a field and 𝑋 be some set. The function algebra 𝕂𝑋 ={(}𝑋,𝕂) consists of functions 𝑋 →𝕂 with scaling, addition, and multiplication defined pointwise. falg

Additional structure

• If 𝑋 is a topological space, one may consider a Continuous function algebra.
• If one restricts to maps of finite support one gets the free module of 𝑋 over 𝕂.
  • In particular, if 𝑋 is a group this is the group ring.

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