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An n-Cell as a Generalize Inverse Limit Indexed by the Integers

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Abstract

For each positive integer n, we construct a function \(f:[0, 1]\rightarrow 2^{[0, 1]}\) (which we will call a filled n-stairs function) such that the inverse limit of an inverse sequence of closed unit intervals with f as the only bonding function (indexed by the integers) is an n-cell. This answers the question by R. P. Vernon.

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Funding

This research was supported by the Slovenian Research Agency Project No. P1-0292.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1000, Ljubljana, Slovenia

    Boštjan Lemež

  2. Institute of Mathematics Physics and Mechanics, Jadranska 19, SI-1000, Ljubljana, Slovenia

    Boštjan Lemež

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  1. Boštjan Lemež
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Correspondence to Boštjan Lemež.

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Communicated by Rosihan M. Ali.

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Lemež, B. An n-Cell as a Generalize Inverse Limit Indexed by the Integers. Bull. Malays. Math. Sci. Soc. 45, 1241–1254 (2022). https://doi.org/10.1007/s40840-022-01256-6

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  • DOI: https://doi.org/10.1007/s40840-022-01256-6

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