On inverse limits with set-valued functions on graphs, dimensionally stepwise spaces and ANRs

摘要

A space X is a dimensionally stepwise space if dim X < infinity and for any 1 <= m <= dimX there is an open set Urn of X such that dim U-m = m. In this paper, for given inverse sequence {X-i, f(i,i+1)}(i=1)(infinity) of compacta with upper semi-continuous set-valued functions, we introduce new indexes (I) over tilde({X-i, f(i,i+1)}) and (W) over tilde({X-i, f(i,i+1)}), and by use of the indexes we investigate topological structures of inverse limits of graphs with upper semi-continuous set-valued functions. Especially, we prove the following theorems. (C) 2017 Elsevier B.V. All rights reserved.