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Mar 16, 2023 at 8:52 comment added user43326 Yes, your argument is correct, I am not sure about your question 1, but a quick look at the proof seems to indicate that it should work for any polynomials. As to 2, yes, it is true except for "very bad" sets (from view point of classical algebraic topology), and affine varieties are always good enough.
Mar 16, 2023 at 3:50 history edited Vladimir Zolotov
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Mar 16, 2023 at 3:39 history asked Vladimir Zolotov CC BY-SA 4.0