Vol. 93, No. 2, 1981

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On compact metric spaces with noncoinciding transfinite dimensions

Leonid A. Luxemburg

Vol. 93 (1981), No. 2, 339–386
Abstract

For every no more than countable ordinal number α we shall define an ordinal number φ(α) such that for every compact metric space X with ind X α we have Ind X φ(α) and there exists a compact metric spaces Xα with ind Xα = α, Ind Xα = φ(α), where ind Xα and Ind Xα mean small and large transfinite inductive dimensions respectively. In particular we now extend the author’s previous result on existence of compact metric spaces with noncoinciding transfinite dimensions.

Mathematical Subject Classification 2000
Primary: 54F45
Secondary: 54E35
Milestones
Received: 30 January 1979
Revised: 17 April 1979
Published: 1 April 1981
Authors
Leonid A. Luxemburg