Does there exist a regular closed curve y in the plane R² which cuts the plane into 3 regions, i.e. such that the complement of the image of y in R² consists of 3 connected components? Select one: O a. Yes, there exists such a curve. In fact, there exists a curve with these properties with constant curvature. O b. Yes, there exists such a curve, but any such curve has non-constant curvature. O c. No, no such curve exists, by the Jordan curve theorem. No, no such curve exists, by Hopf's Umlaufsatz. O d. O e. O f. Og. No, no such curve exists, by Green's theorem. Oh. No, no such curve exists, by the four vertex theorem. O i. No, no such curve exists, by Gauss' Theorema Egregium. O j. No, no such curve exists, by the Gauss-Bonnet theorem. No, no such curve exists, by Fenchel's theorem. No, no such curve exists, by the isoperimetric inequality.

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ISBN:9780470458365
Author:Erwin Kreyszig
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Does there exist a regular closed curvey in the plane R² which cuts the plane into 3 regions, i.e. such that the complement of the image of y in R²
consists of 3 connected components?
Select one:
O a. Yes, there exists such a curve. In fact, there exists a curve with these properties with constant curvature.
O b. Yes, there exists such a curve, but any such curve has non-constant curvature.
No, no such curve exists, by the Jordan curve theorem.
No, no such curve exists, by Hopf's Umlaufsatz.
No, no such curve exists, by Fenchel's theorem.
No, no such curve exists, by the isoperimetric inequality.
O c.
O d.
O e.
O f.
Og. No, no such curve exists, by Green's theorem.
Oh. No, no such curve exists, by the four vertex theorem.
No, no such curve exists, by Gauss' Theorema Egregium.
O j. No, no such curve exists, by the Gauss-Bonnet theorem.
O i.
Transcribed Image Text:Does there exist a regular closed curvey in the plane R² which cuts the plane into 3 regions, i.e. such that the complement of the image of y in R² consists of 3 connected components? Select one: O a. Yes, there exists such a curve. In fact, there exists a curve with these properties with constant curvature. O b. Yes, there exists such a curve, but any such curve has non-constant curvature. No, no such curve exists, by the Jordan curve theorem. No, no such curve exists, by Hopf's Umlaufsatz. No, no such curve exists, by Fenchel's theorem. No, no such curve exists, by the isoperimetric inequality. O c. O d. O e. O f. Og. No, no such curve exists, by Green's theorem. Oh. No, no such curve exists, by the four vertex theorem. No, no such curve exists, by Gauss' Theorema Egregium. O j. No, no such curve exists, by the Gauss-Bonnet theorem. O i.
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