| 1. | Euclidean space itself is not compact since it is not bounded.
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| 2. | This led to modern abstract algebraic notions such as Euclidean domains.
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| 3. | The unique factorization of Euclidean domains is useful in many applications.
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| 4. | The most familiar metric space is 3-dimensional Euclidean space.
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| 5. | Historically, surfaces were initially defined as subspaces of Euclidean spaces.
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| 6. | Every manifold has a natural topology since it is locally Euclidean.
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| 7. | The tesseract, along with all hypercubes, tessellates Euclidean space.
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| 8. | However, Euclidean TSP is probably the easiest version for approximation.
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| 9. | Such an object can exist in certain Euclidean 3-manifolds.
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| 10. | Thus in Euclidean coordinates the same fields are described by the functions
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