Example · Undergraduate
Terms
| Term | This example | Why |
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| vector space |
✓ |
The continuous functions on $[0, 1]$ form a real vector space, because sums and real multiples of continuous functions are continuous.
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| module |
✓ |
The continuous functions on $[0, 1]$ form a module over $\reals$, because they form a vector space over $\reals$.
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| algebra (over a field) |
✓ |
The continuous functions on $[0, 1]$ form an algebra over $\reals$, because the pointwise product $(f g)(x) = f(x) g(x)$ of continuous functions is continuous and bilinear.
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