- #1
moh salem
- 21
- 0
1/ Prove that the set-valued map F defined by
F : [0, 2π] ⇒ R2 as
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".
I would like illustrate that and thank you.
F : [0, 2π] ⇒ R2 as
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".
I would like illustrate that and thank you.