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Depth of dendroids.

Charatonik, Janusz J.; Spyrou, Panayotis — 1994

Mathematica Pannonica

Monotone retractions and depth of continua

Janusz Jerzy Charatonik; Panayotis Spyrou — 1994

Archivum Mathematicum

It is shown that for every two countable ordinals $α$ and $β$ with $α > β$ there exist $λ$ -dendroids $X$ and $Y$ whose depths are $α$ and $β$ respectively, and a monotone retraction from $X$ onto $Y$ . Moreover, the continua $X$ and $Y$ can be either both arclike or both fans.

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