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REFLEXIVITY INDEX AND IRRATIONAL ROTATIONS

Part of: Lattices Miscellaneous applications of functional analysis

Published online by Cambridge University Press:  29 March 2021

BINGZHANG MA Open the ORCID record for BINGZHANG MA [Opens in a new window]  and
K. J. HARRISON Open the ORCID record for K. J. HARRISON [Opens in a new window]
BINGZHANG MA*
Affiliation:
School of Science, East China University of Science and Technology, Shanghai, P. R. China
K. J. HARRISON
Affiliation:
School of Science, Murdoch University, Western Australia6150, Australia e-mail: K.Harrison@murdoch.edu.au
*
e-mail: bingzhangmath@foxmail.com
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Abstract

We determine the reflexivity index of some closed set lattices by constructing maps relative to irrational rotations. For example, various nests of closed balls and some topological spaces, such as even-dimensional spheres and a wedge of two circles, have reflexivity index 2. We also show that a connected double of spheres has reflexivity index at most 2.

Keywords

closed set latticeirrational rotationreflexivity index

MSC classification

Primary: 46N99: None of the above, but in this section
Secondary: 06B30: Topological lattices, order topologies
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 493 - 505
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

This research was partly supported by the National Natural Science Foundation of China (Grant No. 11871021).

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