| Popis: |
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. |
