M|L is Not Closed

Davi Lima; Carlos Matheus; Carlos Gustavo Moreira; Sandoel Vieira

doi:10.1093/imrn/rnaa096

M|L is Not Closed

Davi Lima
, Carlos Matheus
, Carlos Gustavo Moreira
, Sandoel Vieira

Research output: Contribution to journal › Article › peer-review

Abstract

We show that 1 + 3/√ 2 is a point of the Lagrange spectrum L that is accumulated by a sequence of elements of the complement M\L of the Lagrange spectrum in the Markov spectrum M. In particular, M\L is not a closed subset of R, so that a question by T. Bousch has a negative answer.

Original language	English
Pages (from-to)	265-311
Number of pages	47
Journal	International Mathematics Research Notices
Volume	2022
Issue number	1
DOIs	https://doi.org/10.1093/imrn/rnaa096
Publication status	Published - 1 Jan 2022

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title = "M|L is Not Closed",

abstract = "We show that 1 + 3/√ 2 is a point of the Lagrange spectrum L that is accumulated by a sequence of elements of the complement M\textbackslash{}L of the Lagrange spectrum in the Markov spectrum M. In particular, M\textbackslash{}L is not a closed subset of R, so that a question by T. Bousch has a negative answer.",

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N2 - We show that 1 + 3/√ 2 is a point of the Lagrange spectrum L that is accumulated by a sequence of elements of the complement M\L of the Lagrange spectrum in the Markov spectrum M. In particular, M\L is not a closed subset of R, so that a question by T. Bousch has a negative answer.

AB - We show that 1 + 3/√ 2 is a point of the Lagrange spectrum L that is accumulated by a sequence of elements of the complement M\L of the Lagrange spectrum in the Markov spectrum M. In particular, M\L is not a closed subset of R, so that a question by T. Bousch has a negative answer.

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DO - 10.1093/imrn/rnaa096

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SP - 265

EP - 311

JO - International Mathematics Research Notices

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M|L is Not Closed

Abstract

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