A contribution to the topological classification of the spaces Ср(X)

Volume 142 / 1993

Robert Cauty, Tadeusz Dobrowolski, Witold Marciszewski Fundamenta Mathematicae 142 (1993), 269-301 DOI: 10.4064/fm-142-3-269-301


We prove that for each countably infinite, regular space X such that $C_p(X)$ is a $Z_σ$-space, the topology of $C_p(X)$ is determined by the class $F_0(C_p(X))$ of spaces embeddable onto closed subsets of $C_p(X)$. We show that $C_p(X)$, whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set $Ω_α$ for the multiplicative Borel class $M_α$ if $F_0(C_p(X)) = M_α$. For each ordinal α ≥ 2, we provide an example $X_α$ such that $C_p(X_α)$ is homeomorphic to $Ω_α$.


  • Robert CautyUniversité Paris VI
    Analyse Complexe et Géométrie
    4, Place Jussieu
    75252 Paris Cedex 05, France
  • Tadeusz DobrowolskiDepartment of Mathematics
    The University of Oklahoma
    601 Elm Avenue, Room 423
    Norman, Oklahoma 73019-0315, U.S.A.
  • Witold MarciszewskiUniversity of Warsaw
    Banacha 2
    02-097 Warszawa, Poland

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