Some generalizations of distality

Jesus Aponte, Dante Carrasco-Olivera, Keonhee Lee, Carlos Morales


We incorporate the notion of a distal system into the continuum theory \cite{n} through the notion of the {\em 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 \cite{aus} to depend on a given subset of the full set of reparametrizations. Some properties of these reparametrized distality will be obtained.


Distal homeomorphisms; CW-distal homeomorphisms; CW-distal measures; distal flows; proximal cell

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