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S Dec 18, 2015 at 10:01 history bounty ended CommunityBot
S Dec 18, 2015 at 10:01 history notice removed CommunityBot
S Dec 10, 2015 at 8:18 history bounty started probably
S Dec 10, 2015 at 8:18 history notice added probably Draw attention
Dec 9, 2015 at 0:15 history edited probably CC BY-SA 3.0
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Dec 9, 2015 at 0:06 comment added probably Well, actually that thing is motivated by some type of questions where one study some decompositions, of, say, ${\mathbb C}P^n$ into semialgebraic subsets. Here $CP^1$ more or less means space of homogeneous binary forms of degree $1.$ Moreover, i use here operations over complex numbers -- conjugation, inversion -- so it is natural to see it not as $S^2$ but as $CP^1$ with the structure of real algebraic variety.
Dec 8, 2015 at 22:46 comment added Alexandre Eremenko I understand, but then you should not use the notation $CP^1$ if you use the real category.
Dec 8, 2015 at 22:08 comment added probably As we've started from real curve i supposed that we are all the time staying in a real category.
Dec 8, 2015 at 17:02 history edited probably CC BY-SA 3.0
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Dec 8, 2015 at 16:57 comment added probably $CP^1$ has not only structure of complex variety, in which it is as you said, but also a structure of real algebraic variety, where there are a lot more Zarissky closed sets.
Dec 8, 2015 at 13:59 comment added Alexandre Eremenko The only Zarissky closed sets in $CP^1$ are finite sets and the whole $CP^1$. Please edit your question.
Dec 8, 2015 at 10:25 history edited probably CC BY-SA 3.0
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Dec 8, 2015 at 10:03 history edited probably CC BY-SA 3.0
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Dec 8, 2015 at 9:57 history edited probably CC BY-SA 3.0
Added a weaker version of a question.
Dec 8, 2015 at 7:52 history edited probably CC BY-SA 3.0
edited title
Dec 8, 2015 at 7:45 history asked probably CC BY-SA 3.0