Menger spaces and inverse limits

Dennis J. Garity, James P. Henderson and David G. Wright

Vol. 131 (1988), No. 2, 249–259

DOI: 10.2140/pjm.1988.131.249

Abstract

M. Bestvina in 1984 characterized the Menger universal n-dimensional spaces. This characterization is used to identify certain inverse sequences having inverse limit homeomorphic to one of the Menger spaces. Specific models of the Menger spaces are then constructed in the Hilbert Cube as inverse limits of polyhedra. The union of these models is shown to be homeomorphic to the countably infinite dimensional space σ.

Mathematical Subject Classification 2000

Primary: 54F45

Secondary: 57N20, 54B25

Milestones

Received: 29 September 1986

Published: 1 February 1988