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    In de Sitter's solution, space is closed in a topological... — Carmelics
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    In de Sitter's solution, space is closed in a topological sense.

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The sphere has two infinitely distant 'seams': the infinitely distant past and the infinitely distant future.
      ?

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    • 2.Having two such connected infinitely distant seams is the most prominent topological property of the sphere.
      ?

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    • 3.De Sitter's solution shares this spherical topology.
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.De Sitter space admits multiple topologically distinct global representations, including non-compact ones with open spatial sections.
      ?

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    • 2.The choice of topology in de Sitter space reflects a choice of global identification, not an intrinsic feature of the local metric solution.
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    • 3.Weyl's inference from spherical embedding geometry to closed topology conflates the geometry of a particular coordinatization with intrinsic topological structure.
      ?

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    Reason against 2 of 2
    ?
    • 1.Felix Klein and others established that the same local metric geometry is compatible with distinct global topologies via quotienting and covering space constructions.
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    • 2.The 'seams' Weyl identifies as topological features are coordinate-dependent artifacts of the static de Sitter chart, not invariant properties of the manifold.
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    Related

    De Sitter space admits multiple topologically distinct global representations, i...De Sitter's solution shares this spherical topology.Felix Klein and others established that the same local metric geometry is compat...Having two such connected infinitely distant seams is the most prominent topolog...
    +4 moreShow less
    The 'seams' Weyl identifies as topological features are coordinate-dependent art...The choice of topology in de Sitter space reflects a choice of global identifica...The sphere has two infinitely distant 'seams': the infinitely distant past and t...Weyl's inference from spherical embedding geometry to closed topology conflates ...

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    SEP: weyl
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    The sphere has the same degree of metric homogeneity as the world of the special theory of relativity, which can be conceived as a four-dimensional “plane” in the same space. The plane, however, has only one connected infinitely distant “seam,” while it is the most prominent topological property of the sphere to be endowed with two—the infinitely distant past and the infinitely distant future. In this sense one may say that space is closed in de Sitter’s solution. On the other hand, howev
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    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit