A dimensional property of Cartesian product

Volume 220 / 2013

Michael Levin Fundamenta Mathematicae 220 (2013), 281-286 MSC: Primary 55M10; Secondary 54F45, 55N45. DOI: 10.4064/fm220-3-7


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.


  • Michael LevinDepartment of Mathematics
    Ben Gurion University of the Negev
    P.O.B. 653
    Be'er Sheva 84105, Israel

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