Year: 2026
Type: preprint
Abstract: This paper investigates the open cover specification property and its role in the study of topological dynamical systems. We show that this property is a topological invariant and a natural extension of the classical topological specification property from uniform spaces to general topological spaces, and that it is preserved under infinite products with compositions. We further prove that on regular spaces, the strong open cover specification property implies Devaney chaos, and that on locally compact, first countable Hausdorff spaces, it guarantees both distributional chaos and Li Yorke chaos. These results demonstrate the significance of the open cover specification property in linking topological structure with dynamical complexity.
Source: arXiv (Cornell University)
Institution: University of Delhi
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: University Grants Commission
OpenAlex ID: W7203912634
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