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doc/paper/paper.md
@@ -178,8 +178,8 @@ mappings back to the reference element.
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## Modes and Spaces
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To perform calculus operations, each reference element can be equipped with
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-(finite-dimensional) function spaces described by the `FunctionSpace` class.
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-These represent a finite-dimensional space functions $\phi_i: D \to
+function spaces described by the `FunctionSpace` class.
+These represent a finite-dimensional space of functions $\phi_i: D \to
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\mathbb{R}$, where $D$ is the reference element domain, but make no specific
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choice of basis. The function spaces mirror the shape definitions and are
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intended to work in tandem. In fact, the `space_for_shape` function provides a
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