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Investigation reveals equivalence between equicontinuity and distality for non-autonomous systems on the interval, suggesting important insights into system behavior.
In this paper, we investigate equicontinuity and distality for non-autonomous systems on the interval. We investigate distality of the system using the enveloping cover E0(X) = {?k : k ? Z}. We prove that if a sequence of homeomorphisms on the interval (fn) converges to an injective function, then the sequence (f?1,n) converges to a continuous surjective function. Consequently, we establish equivalence of distality and equicontinuity for non-autonomous systems on the interval.
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Yadav et al. (2025) studied this question.
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