Example · Undergraduate
Terms
| Term | This example | Why |
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| metric space |
✓ |
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| normed space |
✓ |
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| Banach space |
✓ |
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| inner product space |
✓ |
$\reals^n$ with the Euclidean norm is an inner product space, because the norm comes from the dot product.
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| hilbert space |
✓ |
$\reals^n$ with the Euclidean norm is complete, as is every finite-dimensional normed space, so it is a Banach space and a Hilbert space.
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| locally compact |
✓ |
Every point has a closed ball around it, which is compact.
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