Geodesic
A contribution to the topological classification of the spaces Ср(X)
Robert Cauty1 ; Tadeusz Dobrowolski2 ; Witold Marciszewski3
1 Université Paris VI Analyse Complexe et Géométrie 4, Place Jussieu 75252 Paris Cedex 05, France
2 Department of Mathematics The University of Oklahoma 601 Elm Avenue, Room 423 Norman, Oklahoma 73019-0315, U.S.A.
3 University of Warsaw Banacha 2 02-097 Warszawa, Poland
Fundamenta Mathematicae, Tome 142 (1993) no. 3, pp. 269-301.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $Ω_α$.
DOI : 10.4064/fm-142-3-269-301
Keywords: function space, pointwise convergence topology, absorbing sets, Borel and projective filters

Robert Cauty 1 ; Tadeusz Dobrowolski 2 ; Witold Marciszewski 3

1 Université Paris VI Analyse Complexe et Géométrie 4, Place Jussieu 75252 Paris Cedex 05, France
2 Department of Mathematics The University of Oklahoma 601 Elm Avenue, Room 423 Norman, Oklahoma 73019-0315, U.S.A.
3 University of Warsaw Banacha 2 02-097 Warszawa, Poland 
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Robert  Cauty; Tadeusz Dobrowolski; Witold Marciszewski. A contribution to the topological classification of the spaces Ср(X). Fundamenta Mathematicae, Tome 142 (1993) no. 3, pp. 269-301. doi : 10.4064/fm-142-3-269-301. http://geodesic.mathdoc.fr/articles/10.4064/fm-142-3-269-301/

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