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Donu Arapura
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Personally, I was never a big fan of the Bourbaki convention of including the Hausdorff axiom into compactness. I would be happy if we dropped the "quasi", but perhaps it would lead to too much confusion at this point in time. On the other hand, schemes were once called preschemes, so algebraic geometers are capable of change.

(This topic is a bit a diversion I think, and I'm not seriously suggesting that the terminology should be changed in this instance. In general, however, I think it is OK to occasionally break with tradition and modify terminology when it's genuinely ungainly. Of course mathematics, like any human endeavor, is full of choices which in hindsight may seem a little odd and perhaps inconsistent. Most of us can live with that. As a complex geometer, I am happy to use "Riemann surface" and "elliptic curve" in the same sentence.)

Personally, I was never a big fan of the Bourbaki convention of including the Hausdorff axiom into compactness. I would be happy if we dropped the "quasi", but perhaps it would lead to too much confusion at this point in time. On the other hand, schemes were once called preschemes, so algebraic geometers are capable of change.

Personally, I was never a big fan of the Bourbaki convention of including the Hausdorff axiom into compactness. I would be happy if we dropped the "quasi", but perhaps it would lead to too much confusion at this point in time. On the other hand, schemes were once called preschemes, so algebraic geometers are capable of change.

(This topic is a bit a diversion I think, and I'm not seriously suggesting that the terminology should be changed in this instance. In general, however, I think it is OK to occasionally break with tradition and modify terminology when it's genuinely ungainly. Of course mathematics, like any human endeavor, is full of choices which in hindsight may seem a little odd and perhaps inconsistent. Most of us can live with that. As a complex geometer, I am happy to use "Riemann surface" and "elliptic curve" in the same sentence.)

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Donu Arapura
  • 35.2k
  • 2
  • 94
  • 160

Personally, I was never a big fan of the Bourbaki convention of including the Hausdorff axiom into compactness. I would be happy if we dropped the "quasi", but perhaps it would lead to too much confusion at this point in time. On the other hand, schemes were once called preschemes, so algebraic geometers are capable of change.