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    Mathematical singularities can be treated as limit points... — Carmelics
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    Challenges→The point at the center of a Schwarzschild black hole arguably does not exist as part of space-time

    Mathematical singularities can be treated as limit points or boundary constructions that preserve their membership in an extended space-time manifold.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Mathematical topology allows defining limit points that possess well-defined properties without requiring interior neighborhood structure.
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    • 2.Compactification procedures in differential geometry successfully extend manifolds by adjoining boundary points while preserving continuity.
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    • 3.Physical singularities may represent genuine features of spacetime requiring formal inclusion rather than exclusion or divergence.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Limit points and actual manifold membership are categorically distinct; treating them as equivalent conflates mathematical convenience with ontology.
      ?

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    • 2.Singularities involve undefined curvature or infinite density—properties that resist embedding in any consistently-defined extended structure.
      ?

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    • 3.Boundary constructions like compactification are conventional choices, not discoveries; they don't establish singularities truly 'belong' to spacetime.
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    Related

    Boundary constructions like compactification are conventional choices, not disco...Compactification procedures in differential geometry successfully extend manifol...Limit points and actual manifold membership are categorically distinct; treating...Mathematical topology allows defining limit points that possess well-defined pro...
    +3 moreShow less
    Physical singularities may represent genuine features of spacetime requiring for...Singularities involve undefined curvature or infinite density—properties that re...The point at the center of a Schwarzschild black hole arguably does not exist as...

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