2009/02/17 by Alex Chigogidze, A. Chigogidze, Alexander Dranishnikov +3 · 2 citations
Mathematics · #46M10 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #History #Mathematical Analysis and Transform Methods #Mathematics #Noncommutative geometry #Operator Algebras (math.OA) #Pure mathematics #math.GT #math.OA #msc:46M10
paper · pdf · doi:10.48550/arxiv.0902.3020
published in arXiv (Cornell University) (Cornell University) · 8 pages
arxiv created 2009/02/17 · openalex publication_date 2009/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a short answer to the question in the title: \em dendrits. Precisely we show that the C∗-algebra C(X) of all complex-valued continuous functions on a compactum X is projective in the category \mathcal C1 of all (not necessarily commutative) unital C∗-algebras if and only if X is an absolute retract of dimension dim X ≤ 1 or, equivalently, that X is a dendrit.