a-) Is the following statements TRUE or FALSE? Prove it or give
a counterexample.
i) If f(x) : Rn → R is a convex function, then for
all α ∈ R, the set {x : f(x) ≤ α} is a convex set.
ii) If {x : f(x) ≤ α} is a convex set for all α ∈ R, then f(x)
is a convex function.
b-) Prove that if x* is a vector such that
∇g(x* ) = 0 and ∇2...
Topology
Prove or disprove ( with a counterexample)
(a) The continuous image of a Hausdorff space is Hausdorff.
(b) The continuous image of a connected space is
connected.