\starttext
\startformula
J:\blackboard{R}^\infty \rightarrow \blackboard{R},f \mapsto J[f]
\stopformula

Correct use of `\blackboard`
\startformula
J:{\blackboard R}^\infty \rightarrow {\blackboard R},f \mapsto J[f]
\stopformula

Neo is great.
\startformula
J \colon ℝ^∞ → ℝ, f ↦ J[f]
\stopformula
\stoptext