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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

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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.

Footnotes

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

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