Posted: Tue Oct 26, 2004 3:32 pm Post subject: Upper-hemi-continuous Correspondence
A correspondence is a “rule” which associates to every element a non-empty subset .
A correspondence is said to be upper-hemi- continuous(u.h.c.) at if for every open set containing there exists a neighbourhood of such that for every
Prove the following assertion:
If the correspondence is u.h.c. at x, then the closure of , i.e. the correspondence is u.h.c.
Martin
Frequent VisitorJoined: 19 Jan 2004Posts: 49
Location: Hong Kong
Posted: Tue Oct 26, 2004 8:11 pm Post subject:
One more question: How to prove the following proposition?? (Carathedory):
Let be a subset of . Then every point is the convex combination of some points in , where is the convex hull of (i.e. the smallest convex set containing )
Chan Pak Keung
Joined: 09 May 2004Posts: 16
Posted: Tue Nov 16, 2004 9:52 pm Post subject:
For the first question, if there any extra information about the topological spcaces S and T ?
I can prove under an extra assumption that T is compact Hausdorff.
All times are GMT + 8 Hours
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum