Compact spaces that result from adequate families of sets. (English) Zbl 0869.54003
Topology Appl. 65, No. 3, 257-270 (1995); erratum ibid. 72, No. 2, 99 (1996).
Summary: We consider compact spaces defined by adequate families of sets as well as continuous images of such spaces which are called AD-compact. The class of AD-compact spaces contains all polyadic spaces. We note some general properties of AD-compact spaces. We prove that there are nonpolyadic AD-compact spaces having a strictly positive measure. We also show that some results on Banach spaces \(C(K)\) valid for a dyadic \(K\) may be extended to \(K\) being AD-compact.
MSC:
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 46E15 | Banach spaces of continuous, differentiable or analytic functions |
Keywords:
dyadic space; polyadic space; adequate family; strictly positive measure; Mazur property; realcompact spaceReferences:
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