Complete Erdős space is unstable

Complete Erdős Space Is Unstable

It is proved that the countably infinite power of complete Erdős space Ec is not homeomorphic to Ec. The method by which this result is obtained consists of showing that Ec does not contain arbitrarily small closed subsets that are one-dimensional at every point. This observation also produces solutions to several problems that were posed by Aarts, Kawamura, Oversteegen, and Tymchatyn. In addit...

CHARACTERIZING STABLE COMPLETE ERDŐS SPACE BY Jan

We focus on the space Ec , the countable infinite power of complete Erdős space Ec. Both spaces are universal spaces for the class of almost zerodimensional spaces. We prove that Ec has the property that it is stable under multiplication with any complete almost zero-dimensional space. We obtain this result as a corollary to topological characterization theorems that we develop for Ec . We also...

Mathematical Proceedings of the Cambridge Philosophical Society Complete Erdos Space Is Unstable

It is proved that the countably infinite power of complete Erdős space Ec is not homeomorphic to Ec. The method by which this result is obtained consists of showing that Ec does not contain arbitrarily small closed subsets that are one-dimensional at every point. This observation also produces solutions to several problems that were posed by Aarts, Kawamura, Oversteegen and Tymchatyn. In additi...

Intuitionistic Propositional Logic is Polynomial-Space Complete

Abatraet. It is the purpose of this note to show that the question of whether a given propositional formula is intuitionistically valid (in Brouwer’s sense, in Kripke’s sense, or just provable by Heyting’s rules, see Kreisel[7]) is p-space complete (see Stockmeyer [14]). Our result has the following consequences: (a) There is a simple (i.e. polynomial time) translation of intuitionistic proposi...

Infiniteness of proof ( ) is polynomial - space complete