Extending bonding functions in generalized inverse sequences.

Abstract Given compact metric spaces X 1 and X 2 , closed subsets Y 1 and Y 2 of X 1 and X 2 respectively, and an upper semicontinuous function g : Y 1 ⊸ Y 2 , we define a special kind of extension f : X 1 ⊸ X 2 of the function g and prove some of its properties. Using this special extension, we answer a question stated by Banič, Črepnjak, Merhar and Milutinović. We also introduce the notions of the weak L -extension property and the strong L -extension property of an inverse sequence for any property L of graphs of set-valued functions. We show that, in the case where L means the surjectivity of such graphs, not all inverse sequences of compact metric spaces have the strong L -extension property but they do have the weak L -extension property. [ABSTRACT FROM AUTHOR]