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A characterization of a map whose inverse limit is an arc

Part of: Topological dynamics Low-dimensional dynamical systems Maps and general types of spaces defined by maps Special properties

Published online by Cambridge University Press:  04 May 2021

SINA GREENWOOD  and
SONJA ŠTIMAC
SINA GREENWOOD
Affiliation:
University of Auckland, Private Bag 92019, Auckland, New Zealand (e-mail: sina@math.auckland.ac.nz)
SONJA ŠTIMAC*
Affiliation:
Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia
*
e-mail: sonja@math.hr
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Abstract

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For a continuous function $f:[0,1] \to [0,1]$ we define a splitting sequence admitted by f and show that the inverse limit of f is an arc if and only if f does not admit a splitting sequence.

Keywords

arcinverse limitsingle bonding map

MSC classification

Primary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth) 54F65: Topological characterizations of particular spaces
Secondary: 54C05: Continuous maps 37B45: Continua theory in dynamics 54F15: Continua and generalizations
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 8 , August 2022 , pp. 2533 - 2549
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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