More on continuous closed convex sets

Abstract

Continuous closed convex sets, in the sense of Gale and Klee, have revealed man y prop erties sha red by compact sets. In th is paper, we give sufficient conditions for the closedness of the image of continuo us closed co nvex sets und er a closed co nvex process. We also esta blish the closed ness and th e exactness of the image fun ct ion of a funct ion with co nt inuo us epigra phunder a closed co nvex process. Moreover we provide new cha rac te riza tio ns of closed co nvex continuo us sets in terms of normal co ne, recession co ne. bounded ness a nd infinite distance Finally we study the non emptines s of the inter section of a counta ble family of closed convex sets where every finiteintersection with a closed convex continuous set is nonempty

Keywords:

• Continuous convex set
• Normal cones
• Recession cones
• Convex processes
• Nonempty intersection