Inverse limit – Knowledge and References

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Locally Pseudoconvex Spaces and Algebras

Published in Michael Ruzhansky, Hemen Dutta, Advanced Topics in Mathematical Analysis, 2019

is called the projective (or inverse) limit of that projective system. All algebraic operations in lim←Ai are defined point-wise as in the product ∏i∈IAi and lim←Ai is provided with the subset topology, defined by the product topology of ∏i∈IAi. Then lim←Ai is a TA.

Rank 2 proximal Cantor systems are residually scrambled

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Journal Information

Published in Dynamical Systems, 2018

Takashi Shimomura

We denote an inverse limit as follows: Further, Δ∞ is equipped with product topology. For each n ≥ 0, we denote the projection as ξ∞, n: Δ∞ → Δn. It is evident that ξ∞, n is continuous. For ∞ ≥ k > j > i, it follows that ξj, i○ξk, j = ξk, i.