Mathematics · Topology
Consider the function f: &mathbb;R;2 → &mathbb;R;2 given by f(x, y) = (e2πix cos(2πiy), e2πix sin(2πiy)). Which of the following statements is TRUE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If U is open in &mathbb;R;2, then f(U) is open in &mathbb;R;2✓
- 2If U is closed in &mathbb;R;2, then f(U) is closed in &mathbb;R;2
- 3If U is dense in &mathbb;R;2, then f(U) is dense in &mathbb;R;2
- 4f is surjective
Correct answer
If U is open in &mathbb;R;2, then f(U) is open in &mathbb;R;2
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