Continuous function algebra

Let $𝑋$ be a topological space and $𝕂$ be a topological field. The continuous function algebra $𝐶 𝕂 (𝑋) = 𝖳 𝗈 𝗉 (𝑋, 𝕂)$ is the subalgebra of the Function algebra containing continuous functions, fun i.e. continuous functions $𝑋 \to 𝕂$ with scaling, addition, and multiplication defined pointwise.