| 21. | This bijection respects unitary equivalence and strong containment.
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| 22. | A permutation is simply a bijection from the set of positive integers to itself.
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| 23. | In fact we have a non-natural bijection
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| 24. | An isomorphism is a structure-preserving bijection.
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| 25. | This is an analytic bijection with analytic inverse.
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| 26. | Specifically, the bijection is given by.
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| 27. | By construction, there is a bijection of ring of \ mathcal { X }.
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| 28. | However this reasoning is not constructive, as it still does not construct the required bijection.
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| 29. | The mapping is a linear bijection from onto the range, whose inverse need not be bounded.
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| 30. | The main result is that for any groupoids G, H, K there is a natural bijection
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