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

THE EXTENSION DIMENSION OF UNIVERSAL SPACES

Ivan Ivanšić and Leonard R. Rubin

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_(M_α, T) U = [Sⁿ], and

(b) if U ∈ K, K ∈ T, dim U ≤ K, and U contains a copy of every compact metrizable space X with dim X ≤ K, 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.