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fixed typo, clarified "algebraic"
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YCor
YCor
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A retract algebraic subset of the plane which does not admit an algebraic retraction

What is an example of an algebraic (=Zariski closed) subset  $C$ of $\mathbb{R}^2$ which is a topological retract of $\mathbb{R}^2$, but there is no an algebracialgebraic retraction $P:\mathbb{R}^2 \to C$?

What is an example of such a situation in $\mathbb{C}^2$?

A retract algebraic subset of plane which does not admit an algebraic retraction

What is an example of an algebraic subset  $C$ of $\mathbb{R}^2$ which is a topological retract of $\mathbb{R}^2$ but there is no an algebraci retraction $P:\mathbb{R}^2 \to C$?

What is an example of such a situation in $\mathbb{C}^2$?

A retract algebraic subset of the plane which does not admit an algebraic retraction

What is an example of an algebraic (=Zariski closed) subset $C$ of $\mathbb{R}^2$ which is a topological retract of $\mathbb{R}^2$, but there is no algebraic retraction $P:\mathbb{R}^2 \to C$?

What is an example of such a situation in $\mathbb{C}^2$?

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Ali Taghavi
Ali Taghavi
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A retract algebraic subset of plane which does not admit an algebraic retraction

What is an example of an algebraic subset $C$ of $\mathbb{R}^2$ which is a topological retract of $\mathbb{R}^2$ but there is no an algebraci retraction $P:\mathbb{R}^2 \to C$?

What is an example of such a situation in $\mathbb{C}^2$?