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Conditions which ensure that a simple map does not raise dimension

W. Dębski, J. Mioduszewski (1992)

Colloquium Mathematicae

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...

Connected economically metrizable spaces

Taras Banakh, Myroslava Vovk, Michał Ryszard Wójcik (2011)

Fundamenta Mathematicae

A topological space is non-separably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a non-separably connected complete metric space X under a monotone quotient map. The metric d X of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set d X ( a , b ) : a , b ∈ A does not exceed the density of A, | d X ( A × A ) | ≤ d e n s ( A ) . The construction of the space X determines a functor : Top...

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