33 biholomorphic means that there exists an inverse mapping to a mapping, and both can be differentiable. For example, the sphere S2 matches the union Cν∪Cσ of Cν and Cσ which are homeomorphic with its own open set, and has the biholomorphic mapping w∊Cν∩Cσ↔r=1/ŵ∊Cν∩Cσ between Cν and Cσ, so it is a Riemann surface. However, ŵ is the conjugate complex number of w. And the complex plane C and the open disc D are a Riemann surface where φλ, therefore φµ*φλ-1, becomes an identity mapping. Homeomorphic mapping exists between the complex plane C and the open disc D. In other words, if we look at it as topological space, then C and D can be seen as the same. However, if we look at it as a Riemann surface, then there is no biholomorphic mapping between C and D. Biholomorphic functions which use as their domain the complex plane C which has no boundaries until the far side of infinity cannot have the open disc D which has the finite boundary S1 as their range (save for constant functions).(7) Therefore C and D can be differentiated if we view them as Riemann surfaces. This shows that the difference, where C has no boundaries but D does, in contrast to being ignored when seen as topological space, is decisive when seen as Riemann surfaces. The complex plane C that is the image of the spirit of God and the open disc D that is the image of the soul of Man are the same when see as topological space. The spirit of God and the soul of Man are continuous in that they are both open. Yet C and D are differentiated by whether they have boundaries when seen as Riemann surfaces. The spirit of God is infinite, without boundaries, but the soul of Man is finite, with boundaries. The soul of a person stands as an individual that is clearly demarcated from others, starting with God. NOTES (1) Rice, Richard, The Openness of God, Downers Grove, InterVarsity Press, 1994, pp15-16 (2) Bourbaki, Nicolas, Topologie généraleⅠ, Berlin, Springer, 2007, p1 (3) ibid. pp6-7 (4) ibid. P59 (5) ibid. P62 (6) Donaldson, Simon, Riemann Surfaces, Oxford, Oxford UP, 2011, pp29-30 (7) Stein, Elias M. Complex Analysis, Princeton, Princeton UP, 2003, p50

34 Publizr Home