Topological classification of generalized Knaster continua with finitely many endpoints
by
Sonja Stimac
Graduate School of Economics and Business

In this work we develop a symbolic dynamics method which enables us to study properties of certain classes of inverse limits.

We consider the family of generalized Knaster continua K_s = lim _<-- {[0, 1], T_s}, where T_s\colon [0, 1] --> [0, 1] is a tent function with slope s in (1, 2] and periodic extreme point. Continua of this family are represented as quotient spaces of two-sided admissible sequences of zeros and ones, with respect to a suitable equivalence relation. We study the structure of the composant of the endpoint [`c] related to the kneading sequence of T_s, and prove that the continua K_s and K_t are not homeomorphic if s =/= t.

Date received: February 19, 2003