We show that the cardinality of power homogeneous
is bounded by 2
. This answers a question of J. van Mill, who proved this bound for homogeneous
compacta. We further extend some results of I. Juhász, P. Nyikos and Z. Szentmiklóssy and as a corollary we prove that consistently every power homogeneous
compactum is first countable. This improves a theorem of R. de la Vega who proved this consistency result for homogeneous
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Arhangel’skiį, A. V.
, The structure and classification of topological spaces and cardinal invariants,
Uspekhi Mat. Nauk
(1978), no. 6 (204), 29–84, 272.
Arhangel’skiį A. V., 'The structure and classification of topological spaces and cardinal invariants' (1978) 33Uspekhi Mat. Nauk: 29-84.
Arhangel’skiį A. V.The structure and classification of topological spaces and cardinal invariantsUspekhi Mat. Nauk1978332984)| false