Glasnik Matematicki, Vol. 38, No.1 (2003), 121-127.

THE EXTENSION DIMENSION OF UNIVERSAL SPACES

Ivan Ivanšić and Leonard R. Rubin

Faculty of Electrical Engineering, University of Zagreb, Unska 3, P.O. Box 148, 10000 Zagreb, Croatia
e-mail: ivan.ivansic@fer.hr

Department of Mathematics, University of Oklahoma, 601 Elm Ave., Rm. 423, Norman, OK 73019, USA
e-mail: lrubin@ou.edu


Abstract.   Let α be an infinite cardinal, T denote a class of CW-complexes, K the class of all compact Hausdorff spaces, M the class of all metrizable spaces of weight ≤ α and n ≥ 0. We shall prove that,

(a) if U is a universal metrizable space of covering dimension n and weight ≤ α, then ext-dim_(Mα, T) U = [Sn], and

(b) if UK, KT, dim UK, and U contains a copy of every compact metrizable space X with dim XK, then ext-dim_(K, T) U = [K].

2000 Mathematics Subject Classification.   54C55, 54F45.

Key words and phrases.   Extension theory, extension dimension, dimension, stratifiable space, subspace theorem.


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