INDUCING FUNCTIONS BETWEEN INVERSE LIMITS WITH UPPER SEMICONTINUOUS BONDING FUNCTIONS

摘要

In this paper we introduce the category CU in which the corn pact metric spaces are objects and upper semicontinuous functions from X to 2(Y) are morphisms from X to Y. We also introduce the category ICu of inverse sequences in CU. Then we investigate the induced functions between inverse limits of compact metric spaces with upper semicontinuous bonding functions. We provide criteria for their existence and prove that under suitable assumptions they have surjective graphs. We also show that taking such inverse limits is very close to being a functor (but is not a functor) from ICu to Cu, if morphisms are mapped to induced functions. At the end of the paper we give a useful application of the mentioned results.