Monotone Decompositions of Inverse Limit Spaces Based on Finite Graphs

Author

Robert Paul Roe, Missouri University of Science and TechnologyFollow

Abstract

A Θn,L graph is defined to be a compact, connected, locally connected metric space which is not separated into more than n components by any subcontinuum and no subcontinuum is separated into more than L components by any of its subcontinua. If X is a Θn,L graph and f is a continuous surjection of X onto X, then the inverse limit space (X,f) is a Θn continuum (not necessarily locally connected). Furthermore (X,f) admits a unique minimal monotone, upper semicontinuous decomposition such that the quotient space (X,f)/ is a Θn,L graph if and only if (X,f) contains no indecomposable subcontinua with nonempty interior.

Recommended Citation

R. P. Roe, "Monotone Decompositions of Inverse Limit Spaces Based on Finite Graphs," Topology and its Applications, Elsevier, Jan 1990.

The definitive version is available at https://doi.org/10.1016/0166-8641(90)90040-9

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

0166-8641

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1990 Elsevier, All rights reserved.

Publication Date

01 Jan 1990