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## Main Question or Discussion Point

1/ Prove that the set-valued map F defined by

F : [0, 2π] ⇒ R

F(α) := {λ(cos α, sin α) : λ ≥ 0}.

is continuous,

but not upper semicontinuous at any α ∈ [0, 2π].

2/ What is the fact that " F is continuous if it is both u.s.c. and l.s.c".

F : [0, 2π] ⇒ R

^{2}asF(α) := {λ(cos α, sin α) : λ ≥ 0}.

is continuous,

but not upper semicontinuous at any α ∈ [0, 2π].

2/ What is the fact that " F is continuous if it is both u.s.c. and l.s.c".

**I would like illustrate that and thank you.**