[[Function space]]
# Continuous function algebra

Let $X$ be a [[topological space]] and $\mathbb{K}$ be a [[topological field]].
The **continuous function algebra** $C_{\mathbb{K}}(X) = \Top(X,\mathbb{K})$ is the [[Subalgebra over a field|subalgebra]] of the [[Function algebra]] containing [[Continuity|continuous]] functions, #m/def/anal/fun 
i.e. continuous functions $X \to \mathbb{K}$ with scaling, addition, and multiplication defined pointwise.


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