Archive for Mathematical Logic 47 (3):193-203 (2008)

It is well known that infinite minimal sets for continuous functions on the interval are Cantor sets; that is, compact zero dimensional metrizable sets without isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat Chaos 13:1665–1671, 2003) that infinite minimal sets for continuous functions on connected linearly ordered spaces enjoy the same properties as Cantor sets except that they can fail to be metrizable. However, no examples of such subsets have been known. In this note we construct, in ZFC, ${2^{\mathfrak{c}}}$ non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces
Keywords Dynamical system  Minimal set  Cantor set  Linearly ordered topological space
Categories (categorize this paper)
DOI 10.1007/s00153-008-0069-3
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,784
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Properties of Ideals on the Generalized Cantor Spaces.Jan Kraszewski - 2001 - Journal of Symbolic Logic 66 (3):1303-1320.
On Dp-Minimal Ordered Structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
Partially Ordered Sets and the Independence Property.James H. Schmerl - 1989 - Journal of Symbolic Logic 54 (2):396-401.
Definable Sets in Boolean Ordered o-Minimal Structures. II.Roman Wencel - 2003 - Journal of Symbolic Logic 68 (1):35-51.
Quasi-o-Minimal Structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
Monotone Reducibility and the Family of Infinite Sets.Douglas Cenzer - 1984 - Journal of Symbolic Logic 49 (3):774-782.
A Monotonicity Theorem for Dp-Minimal Densely Ordered Groups.John Goodrick - 2010 - Journal of Symbolic Logic 75 (1):221-238.
Transfer Methods for o-Minimal Topology.Alessandro Berarducci & Margarita Otero - 2003 - Journal of Symbolic Logic 68 (3):785-794.
Lattice Ordered O -Minimal Structures.Carlo Toffalori - 1998 - Notre Dame Journal of Formal Logic 39 (4):447-463.
Weakly o-Minimal Structures and Some of Their Properties.B. Sh Kulpeshov - 1998 - Journal of Symbolic Logic 63 (4):1511-1528.
Expansions of o-Minimal Structures by Iteration Sequences.Chris Miller & James Tyne - 2006 - Notre Dame Journal of Formal Logic 47 (1):93-99.


Added to PP index

Total views
17 ( #622,534 of 2,462,972 )

Recent downloads (6 months)
1 ( #449,363 of 2,462,972 )

How can I increase my downloads?


My notes