We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-1,
author = {Chris Good and Brian E. Raines},
title = {Continuum many tent map inverse limits with homeomorphic postcritical $\omega$-limit sets},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {1-21},
zbl = {1134.37318},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-1}
}
Chris Good; Brian E. Raines. Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets. Fundamenta Mathematicae, Tome 189 (2006) pp. 1-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-1/