Weyl's separation of topological and metrical structure, inherited from Riemann, presupposes a realist reading of manifold structure that Poincaré's géométrie de position explicitly rejects.
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Manifold (in mathematics)(as the object being described by topological and metrical structures)
A mathematical space that looks smooth and flat when you zoom in closely, but can curve or bend when you look at the bigger picture.
Topological structure(as used in mathematics and physics)
The basic shape and connectivity properties of a space that don't change when you stretch or bend it—like how a coffee mug and donut have the same topological structure because they both have one hole.
metrical structure(Distinguished from inertial and causal structure; shown to be derivable from them.)
The geometric or measurement structure of the world, governing distances and intervals.
realist reading(Strawson's approach to understanding Kant)
An interpretation of a theory that emphasizes the independent existence of things—that reality exists whether or not we perceive it.