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created a disambiguation page: spectral geometry
as seen by spectral triple (often inaccurately referred to “noncommutative geometry”)
Why inaccurately ? Spectral triple is an approach from noncommutative geometry. Noncommutative geometry is a method, point of view. It can be applied to commutative world, and most important work in the subject that in fact aims to.
Inaccurately because the notion of spectral triple is much finer than the notion of NCG. Connes speaks of “metric NCG” sometimes to reflect this.
So in your opinion, the noncommutative geometry should denote just some vanilla topological version without any structures on the spaces ? Then call it noncommutative topology (not the best term, but for this discussion yes). Noncommutative geometry is IMHO (and in practice of many noncommutative geometers) a subject which looks at all kinds of geometrical structures on spaces locally associated to duals of noncommutative algebras of various kinds and categorical levels and possibly with additional structures.
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