Abstract
A compact space is called a Dugundji compactum if for every compact containing , there exists a linear extension operator which preserves nonnegativity and maps constants into constants. It is known that every compact group is a Dugundji compactum. In this paper we show that compacta connected in a natural way with topological groups enjoy the same property. For example, in each of the following cases, the compact space is a Dugundji compactum: 1) is a retract of an arbitrary topological group; 2) , where is a pseudocompact space on which some -bounded topological group acts transitively and continuously. Bibliography: 57 titles.
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