# Sh:668

- Shelah, S. (2004).
*Anti-homogeneous partitions of a topological space*. Sci. Math. Jpn.,**59**(2), 203–255. arXiv: math/9906025 MR: 2062196 -
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. - Version 2006-03-11_10 (70p) published version (53p)

Bib entry

@article{Sh:668, author = {Shelah, Saharon}, title = {{Anti-homogeneous partitions of a topological space}}, journal = {Sci. Math. Jpn.}, fjournal = {Scientiae Mathematicae Japonicae}, volume = {59}, number = {2}, year = {2004}, pages = {203--255}, issn = {1346-0862}, mrnumber = {2062196}, mrclass = {03E35 (03E02 03E04 03E55 54A35)}, note = {\href{https://arxiv.org/abs/math/9906025}{arXiv: math/9906025}}, specialissue = {Special issue on set theory and algebraic model theory}, arxiv_number = {math/9906025}, keyword = {set theory, general topology, partition calculus, pcf theory} }