A dimensional property of Cartesian product
Volume 220 / 2013
Fundamenta Mathematicae 220 (2013), 281-286
MSC: Primary 55M10; Secondary 54F45, 55N45.
DOI: 10.4064/fm220-3-7
Abstract
We show that the Cartesian product of three hereditarily infinite-dimensional compact metric spaces is never hereditarily infinite-dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the author) essentially relies on algebraic topology.
