The Bolzano property and the cube-like complexes

Przemysław Tkacz

DOI: http://dx.doi.org/10.12775/TMNA.2017.003

Abstract


Introducing the \emph{Bolzano property}, we present a topological version of the Poincaré-Miranda theorem. One simple, and one algorithmic proof that $n$-cube-like complexes have this property are given. Moreover, we investigate under what conditions the inverse limit preserves the Bolzano property. Finally, we give a characterization of the Bolzano property for locally connected spaces.

Keywords


Simplicial complex; fixed point; cube-like; Poincaré-Miranda

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