On dimensionally exotic maps

Alexander Dranishnikov, Michael Levin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We call a value y = f(x) of a map f: X → Y dimensionally regular if dimX ≤ dim(Y × f−1(y)). It was shown in [6] that if a map f: X → Y between compact metric spaces does not have dimensionally regular values, then X is a Boltyanskii compactum, i.e., a compactum satisfying the equality dim(X × X) = 2dim X − 1. In this paper we prove that every Boltyanskii compactum X of dimension dim X ≥ 6 admits a map f: X → Y without dimensionally regular values. We show that the converse does not hold by constructing a 4-dimensional Boltyanskii compactum for which every map has a dimensionally regular value.

Original languageEnglish
Pages (from-to)967-987
Number of pages21
JournalIsrael Journal of Mathematics
Volume201
Issue number2
DOIs
StatePublished - 2 Oct 2014

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