Eric van Douwen produced in 1993 a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of . We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).
We show that every retral continuum with the fixed point property is locally connected. It follows that an indecomposable continuum with the fixed point property is not a retract of a topological group.
Dado un espacio T3α (X,T), es posible obtener una compactificación T2 del mismo, mediante ultrafiltros asociados a ciertas bases distinguidas de cerrados de (X,T) (Frink [4]). Se plantea así el problema siguiente: ¿Puede obtenerse toda compactificación T2 de (X,T) por este método? Desde el año 1964 en que Frink lo planteó, este interrogante ha tenido respuestas afirmativas parciales. Sin embargo, la solución definitiva es negativa.
The class of ultrasmooth dendroids is contained in the class of smooth dendroids and contains the class of locally connected dendroids. In this paper we study relationships between ultrasmoothness and smoothness in dendroids and we characterize ultrasmooth dendroids.