2021
DOI: 10.1007/s00020-021-02678-w
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Bunce-Deddens Algebras as Quantum Gromov-Hausdorff Distance Limits of Circle Algebras

Abstract: We show that Bunce-Deddens algebras, which are AT-algebras, are also limits of circle algebras for Rieffel's quantum Gromov-Hausdorff distance, and moreover, form a continuous family indexed by the Baire space. To this end, we endow Bunce-Deddens algebras with a quantum metric structure, a step which requires that we reconcile the constructions of the Latrémolière's Gromov-Hausdorff propinquity and Rieffel's quantum Gromov-Hausdorff distance when working on order-unit quantum metric spaces. This work thus cont… Show more

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Cited by 4 publications
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“…Mathematics is a subject published at all levels of education, from elementary to high school (Hutajulu et al, 2019;Meiliasari et al, 2021) l. Based on the Law of the Republic of Indonesia number 20 of 2003 concerning the National Education System Chapter X Article 37 paragraph 1 states that the primary and secondary education curriculum must contain mathematics (Aguilar et al, 2022;Inganah et al, 2023;. Students at the elementary school education level only know arithmetic (Tokgoz et al, 2021).…”
Section: Introductionmentioning
confidence: 99%
“…Mathematics is a subject published at all levels of education, from elementary to high school (Hutajulu et al, 2019;Meiliasari et al, 2021) l. Based on the Law of the Republic of Indonesia number 20 of 2003 concerning the National Education System Chapter X Article 37 paragraph 1 states that the primary and secondary education curriculum must contain mathematics (Aguilar et al, 2022;Inganah et al, 2023;. Students at the elementary school education level only know arithmetic (Tokgoz et al, 2021).…”
Section: Introductionmentioning
confidence: 99%