Upper/ Lower Hemi-Continuous

1. f: X → Y is upper hemi-continuous if

  1) it has a closed graph and

  2) the image of is compact.


2. f: X → Y is lower hemi-continuous if

  1) x_n ∈ X converges to x* ∈ X and

  2) y* ∈ f (x*),

then there exists a sequence {y_n}_n and N such that y_n ∈ f(x_n) for all n ≧ N, and y_n converges to y*.


3. f: X → Y is continuous if it is both upper and lower hemi- continuous.

www.econ.yale.edu/~go49/pdfs/ECON 201/NoteUHC.pdf