| 41. | The M�bius transformations are the only invertible meromorphic functions on the complex plane.
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| 42. | In fact if the imaginary part of is positive, then is invertible since
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| 43. | If " x " is invertible and so everywhere by density.
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| 44. | Given in, pick so that and are invertible.
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| 45. | In other words, it becomes invertible, and the solution becomes unique.
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| 46. | The same definition holds in any invertible element.
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| 47. | The automorphisms of this subgroup are therefore given by the invertible linear transformations, so
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| 48. | To prove that every element of is invertible, we may proceed as follows.
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| 49. | The inverse function of a composition ( assumed invertible ) has the property that.
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| 50. | The invertible sheaves in those theories are in effect the line bundles appropriately formulated.
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