On Arhangelskii's Problem

Saharon Shelah

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On Arhangelskii's Problem

Saharon Shelah

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Abstract

We prove the consistency (modulo supercompact) of a negative answer to Arhangelskii's problem (some Hausdorff compact space cannot be partitioned to two sets not containing a closed copy of Cantor discontinuum). In this model we have CH. Without CH we get consistency results using a pcf assumption, close relatives of which are necessary for such results.

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BibTeX RIS

Saharon Shelah. 1999-06-03. On Arhangelskii's Problem. https://arxiv.org/abs/math/9906025

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