Isac’s Cones

Abstract

This is a very short research work representing an homage to the regretted Professor George Isac, Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. 17000, Kingston, Ontario, Canada, K7K 7B4. Professor Isac introduced the notion of “nuclear cone” in 1981, published in 1983 and called later as “supernormal cone” since it appears stronger than the usual concept of “normal cone”. For the first time, we named these convex cones as “Isac’s Cones” in 2009 , after the acceptance on professor Isac’s part. This study is devoted to Isac’s cones, including significant examples, comments and several pertinent references, with the remark that this notion has its real place in Hausdorff locally convex spaces not in the normed linear spaces, having strong implications and applications in the efficiency and optimization. Isac’s cones represent the largest class of convex cones discovered till now in separated locally convex spaces ensuring the existence and important properties for the efficient points under completeness instead of compactness.