Compact spaces that result from adequate families of sets

  • Plebanek G
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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. © 1995.

Author-supplied keywords

  • Adequate family
  • Dyadic space
  • Mazur property
  • Polyadic space
  • Realcompact space
  • Strictly positive measure

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  • Grzegorz Plebanek

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