While a localised sphere exhibits non-euclidean geometry, a
cosmological 'sphere' does not exhibit non-euclidean geometry.

Cosmological geometry (the cosmological framework, the universe, etc.)
is not represented by local geometry (euclidean and non-euclidean).
While a localised sphere exhibits non-euclidean geometry, a
cosmological 'sphere' does not exhibit non-euclidean geometry.

Underpinning any geometry is the localizability of its elements. In a
cosmological geometry, this localizability is absent. Thus for any
cosmological space, we find the absence of geometrical differences,
whereas in local space we find any number of geometrical differences.

Underpinning the localizability of the elements of geometry is the
supportive framework for positions. We can now turn to the nature of
cosmological geometry, which in this case is our framework. This is
not itself geometrical nor is it of the nature of a position-- as a
framework it exhibits no properties. It is, accordingly, not an object
itself, but the means by which objects or points, or positions, can
beconsidered at all. Geometry is founded on it.