PG entrance exam IIT JAM 2025 Mock Test Mathematical Science

Let f : ℝn → ℝn be a continuously differentiable map satisfying ||f(x) - f(y)|| ≥ ||x − y||, for all x, y ∈ ℝn. Then 

1
f is onto
2
f(ℝn) is a closed subset of ℝn
3
f(ℝn) is an open subset of ℝn 
4
f(0) = 0
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