We incorporate the notion of a distal system into the continuum theory  through the notion of the continuum-wise distal homeomorphism. Results concerning distal homeomorphisms will be generalized to the case of cw-distal homeomorphisms. Notions of cw-distality for measures will be studied. We also analyze the variation of distality for flows obtained by making the proximal cell  to depend on a given subset of the full set of reparametrizations. Some properties of these reparametrized distality will be obtained.
"Some generalizations of distality." Topol. Methods Nonlinear Anal. 55 (2) 533 - 552, 2020. https://doi.org/10.12775/TMNA.2019.100