Abstract
We prove that every isometric copy of C(L) in C(K) is complemented if L is a compact Hausdorff space of finite height and K is a compact Hausdorff space satisfying the extension property, i.e., every closed subset of K admits an extension operator. The space C(L) can be replaced by its subspace C(L|F) consisting of functions that vanish on a closed subset F of L. We also study the class of spaces having the extension property, establishing some stability results for this class and relating it to other classes of compact spaces.
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The first author is sponsored by FAPESP (Process No. 2012/25171-0).
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Correa, C., Tausk, D.V. Extension Property and Complementation of Isometric Copies of Continuous Functions Spaces. Results. Math. 67, 445–455 (2015). https://doi.org/10.1007/s00025-014-0411-5
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DOI: https://doi.org/10.1007/s00025-014-0411-5