Characterizing global properties in inverse limits

Zvonko Cerin

Vol. 112 (1984), No. 1, 49–68

DOI: 10.2140/pjm.1984.112.49

Abstract

This paper presents necessary and sufficient conditions, in terms of properties of bonding maps and bonding spaces, on an inverse sequence X = {X_i,p_ii+1} of compact metric spaces in order that its inverse limit X = X is either an approximate absolute neighborhood retract, an (internally) e-calm compactum, an absolute neighborhood retract, an LCⁿ compactum, or that X has (covering) dimension ≤ n.

Mathematical Subject Classification

Primary: 54F40, 54F40

Secondary: 54F43

Milestones

Received: 12 April 1982

Revised: 15 September 1982

Published: 1 May 1984