Inverse Limits In A General Setting
Abstract
In this chapter we investigate inverse limits in a very general setting: over directed sets with factor spaces that are compact Hausdorff spaces using upper semi-continuous closed set-valued bonding functions. Basic existence and connectedness theorems are proved and examples are provided that illustrate limitations to the generality of the theorems. One section is devoted to examples in the case where the factor spaces are all the interval [0, 1]. Basic theorems on mappings of inverse limits are included as well. As the chapter progresses additional hypotheses are added to the factor spaces (up to compact metric) and the bonding functions (continuous single-valued or unions of such). The chapter concludes with considerations of a few miscellaneous topics including dimension and a proof that a 2-cell is not an inverse limit with a single upper semi-continuous function on [0, 1]. © Springer Science+Business Media, LLC 2012.
Recommended Citation
W. T. Ingram and W. S. Mahavier, "Inverse Limits In A General Setting," Developments in Mathematics, vol. 25, pp. 75 - 129, Springer, Apr 2012.
The definitive version is available at https://doi.org/10.1007/978-1-4614-1797-2_2
Department(s)
Mathematics and Statistics
International Standard Book Number (ISBN)
978-146141796-5
International Standard Serial Number (ISSN)
1389-2177
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 Springer, All rights reserved.
Publication Date
16 Apr 2012
