Small retractions of smooth dendroids onto trees
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.
Certain equivalences of Mrowka's separating condition enable us to characterize when parametric maps are open, closed or quotient.
We give an affirmative answer to Schauder's fixed point question.
Let E be the total space of a Hurewicz fiber space whose base and all fibers are ANRs. We prove that if E is metrisable, then it is also an ANR.
In this note we characterize the c-paracompact and c-collectionwise normal spaces in terms of continuous selections. We include the usual techniques with the required modifications by the cardinality.
The aim of this paper is to continue the study of θ-irresolute and quasi-irresolute functions as well as to give an example of a function which is θ-irresolute but neither quasi-irresolute nor an R-map and thus give an answer to a question posed by Ganster, Noiri and Reilly. We prove that RS-compactness is preserved under open, quasi-irresolute surjections.