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

The present paper establishes a new homotopy, called an LMA-homotopy, and further, an LMA-homotopy equivalence suitable for studying the homotopic properties of both Euclidean topology and M-topology. Indeed, the LMA-map (see Definition 12 of the present paper) is an advanced version of that of [18]. Besides, the paper studies relations among an ordinary homotopy equivalence (resp. contractibility) for spaces (X,UX), an LMA-homotopy equivalence (resp. LMA-contractibility) for spaces (X,UX) and an MA-homotopy equivalence (resp. MA-contractibility) for MA-spaces. Finally, we classify (X,UX) in terms of the LMA-homotopy equivalence. This approach will facilitate studies of applied topology, approximation theory and digital geometry.