Mobs, trees, and fixed points

Weak Cutpoint Ordering on Hereditarily Unicoherent Continua

“…Our interest in such partial orderings stems from the fact (Hunter [l]) that a one-dimensional compact connected semigroup with zero and unit admits such a partial ordering. Ward [5] has studied a class of partially ordered spaces, called generalized trees, which he characterized as hereditarily unicoherent continua which admit a closed, order-dense partial order with unique minimal element. We improve his characterization by replacing "order dense'' by the weaker "monotone,"…”

On dendritic sets

“…Introduction. In earlier papers [5], [6], [7] the author characterized various types of acyclic continua in terms of their inherent order theoretic properties, and the present work is concerned with the same problem for connected and acyclic spaces which are not necessarily compact. Such spaces, if they are locally connected, are termed dendritic.…”