We investigate if a unital C(X)-algebra is properly infinite when all its fibres are properly infinite. We show that this question can be rephrased in several different ways, including the question of whether every unital properly infinite C*-algebra is K1-injective. We provide partial answers to these questions, and we show that the general question on proper infiniteness of C(X)-algebras can be reduced to establishing proper infiniteness of a specific C([0,1])-algebra with properly infinite fibres.
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Étienne Blanchard, Randi Rohde, Mikael Rørdam, Properly infinite <var>C</var>(<var>X</var>)-algebras and <var>K</var><sub>1</sub>-injectivity. J. Noncommut. Geom. 2 (2008), no. 3, pp. 263–282DOI 10.4171/JNCG/21