Abstract
Introducing the 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.
Citation
Przemysław Tkacz. "The Bolzano property and the cube-like complexes." Topol. Methods Nonlinear Anal. 49 (2) 481 - 495, 2017. https://doi.org/10.12775/TMNA.2017.003
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