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Peer-reviewedCC BY 4.0Mathematics

Topological Spaces with Low Reflexivity Indices

  • Don W. Hadwin1
  • Ken J. Harrison2
  • Eric A. Nordgren1
  • Junhao Shen1
  1. 1Mathematics Department, University of New Hampshire, Durham, NH 03824, USA
  2. 2School of Information Technology, Murdoch University, Perth, WA 6150, Australia
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Abstract

We determine the reflexivity indices of certain topological spaces. The reflexivity index is a measure of certain type of dynamical complexity of the space. The reflexivity index is 1 exactly when there is a continuous selfmap on the space so that the orbit at each point is dense in the space. Spaces with index 1 include the rational numbers, the irrational numbers, an n-torus with 1≤n≤2ℵ0, and X∖0 where X is any infinite-dimensional separable Banach space. The index of 0,1 and Rn (n∈N) is 2.

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Cite

BibTeXRIS
BibTeX
@article{hadwin2026topological,
  title = {{Topological Spaces with Low Reflexivity Indices}},
  author = {Don W. Hadwin and Ken J. Harrison and Eric A. Nordgren and Junhao Shen},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14193586},
  url = {https://www.mdpi.com/2227-7390/14/19/3586},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Topological Spaces with Low Reflexivity Indices
AU  - Don W. Hadwin
AU  - Ken J. Harrison
AU  - Eric A. Nordgren
AU  - Junhao Shen
PY  - 2026
DA  - 2026/10/02
JO  - Mathematics
DO  - 10.3390/math14193586
UR  - https://www.mdpi.com/2227-7390/14/19/3586
AB  - We determine the reflexivity indices of certain topological spaces. The reflexivity index is a measure of certain type of dynamical complexity of the space. The reflexivity index is 1 exactly when there is a continuous selfmap on the space so that the orbit at each point is dense in the space. Spaces with index 1 include the rational numbers, the irrational numbers, an n-torus with 1≤n≤2ℵ0, and X∖0 where X is any infinite-dimensional separable Banach space. The index of 0,1 and Rn (n∈N) is 2.
SN  - 2227-7390
ER  -