Abstract

Given a homogeneous compactum X, a general method of constructing homogeneous compacta as inverse limit spaces lim{Xn, bn} is introduced, where Xn are covering spaces for X and bn are covering mappings. If [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] is the Menger universal curve, a variant of this construction provides a homogeneous, arcwise connected, non-locally connected curve. This answers a question of K. Kuperberg.

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