1974/01/01 by Robert J. Sacker, George R. Sell · 1 citation
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology
paper · doi:10.1090/s0002-9947-1974-0350715-8
openalex publication_date 1974/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
In this paper we shall study homomorphisms <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p colon upper W right-arrow upper Y"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>:</mml:mo> <mml:mi>W</mml:mi> <mml:mo stretchy="false"> → </mml:mo> <mml:mi>Y</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">p:W → Y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on minimal transformation groups. We shall prove, in the case that <italic>W</italic> and <italic>Y</italic> are metrizable, that <italic>W</italic> is a finite ( <italic>N</italic> -to-1) extension of <italic>Y</italic> if and only if <italic>W</italic> is an <italic>N</italic> -fold covering space of <italic>Y</italic> and <italic>p</italic> is a covering map. This result places no further restrictions on the acting group. We shall then use this characterization to investigate the question of lifting an equicontinuous structure from <italic>Y</italic> to <italic>W</italic> . We show that, under very weak restrictions on the acting group, this lifting is always possible when <italic>W</italic> is a finite extension of <italic>Y</italic> .