On topological types of the simplest indecomposable continua
The additivity of the volume and Sperner's lemma
Another geometric proof of supercompactness of compact metric spaces
Simple plane images of the Sierpiński triangular curve are nowhere dense
Conditions which ensure that a simple map does not raise dimension
The present paper deals with those continuous maps from compacta into metric spaces which assume each value at most twice. Such maps are called here, after Borsuk and Molski (1958) and as in our previous paper (1990), simple. We investigate the possibility of decomposing a simple map into essential and elementary factors, and the so-called splitting property of simple maps which raise dimension. The aim is to get insight into the structure of those compacta which have the property that simple maps...
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