Homotopic properties of an MA-digitization of 2D Euclidean spaces

作者：

Highlights：

• Development of a new homotopy suitable for digitizing 2D Euclidean topological spaces.

• Establishment of a new homotopy, called an LMA-homotopy, and further, an LMA-homotopy equivalence.

• Comparison among an ordinary homotopy equivalence an LMA-homotopy equivalence and an MA-homotopy.

• Finally, we classify 2D Euclidean spaces in terms of the LMA-homotopy equivalence.

摘要

•Development of a new homotopy suitable for digitizing 2D Euclidean topological spaces.•Establishment of a new homotopy, called an LMA-homotopy, and further, an LMA-homotopy equivalence.•Comparison among an ordinary homotopy equivalence an LMA-homotopy equivalence and an MA-homotopy.•Finally, we classify 2D Euclidean spaces in terms of the LMA-homotopy equivalence.

论文关键词：Marcus–Wyse topology,Digital topology,MA-digitization,M-localized neighborhood,LMA-homotopy equivalence,MA-homotopy equivalence,LMA-contractibility,MA-contractibility

论文评审过程：Received 9 August 2016, Revised 13 May 2017, Accepted 1 July 2017, Available online 20 July 2017, Version of Record 30 April 2018.

论文官网地址：https://doi.org/10.1016/j.jcss.2017.07.003