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Rosenthal compact

Last-modified: 2010-08-31 (火) 09:43:46

Definition Edit

  • Let K be a compact Hausdorff space. K is a Rosenthal compact iff K is homeomorphic to a pointwise compact set of functions of first Baire class on a Polish space.

Property Edit

  • The product of two Rosenthal compacts is a Rosenthal compact.
  • Every compact metric space is Rosenthal compact.

Reference Edit

  • Edgar, G. A. and Wheeler, R. F. , Topological properties of Banach spaces, Pacific J. Math. 115 (1984), no. 2, 317--350.