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Question Number 1456 by 123456 last updated on 06/Aug/15

S^{1} = {(x, y) \in R^{2} : x^{2} + y^{2} = 1}

φ : [0, 4 π) \to E^{1, 1}, E^{1, 1} \subset R^{2}

φ (t) = (1 + \cos t \sin t) (\cos t, \sin t)

S^{1} \cap E^{1, 1} \neq \emptyset

1 . is φ injective into E^{1, 1}

2 . can φ^{- 1} : E^{1, 1} \to [0, 4 π) be continuous ?