Is the following a "consistent non-Euclidean geometry"? It seems to satisfy the first 4 Euclidean postulates. Any comments? Any agreements or disagreements?

Following are the additional conditions on the geometry: ( Please note in Elliptical geometry: points at each other's antipodes are considered to be the same point as explained in this wiki link: http://en.wikipedia.org/wiki/Elliptic_geometry#The_spherical_model)

1.Elliptical model(2D) - Right side quarter sphere including half of the equator below 2D quarter sphere included.

2.Elliptical model(1D) - Blue Arc on left, with equator point removed

3.Half latitude line - Yellow dotted line for easy visualization (Not exactly to the scale.). One can consider any point on 1D blue arc, to be the same as any point on the corresponding half constant latitude(parallel) line. This condition is inspired by Elliptical geometry's "antipodes points are same(identification)" condition.

Mixed dimension non-Euclidean geometry example

  • $\begingroup$ This seems to be an example of pseudo metric space. $\endgroup$ – user114736 Jan 19 '14 at 18:24

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