A contribution to the topological classification of the spaces Ср(X)
Fundamenta Mathematicae, Tome 142 (1993) no. 3, pp. 269-301
Cet article a éte moissonné depuis 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 $Ω_α$.
Keywords:
function space, pointwise convergence topology, absorbing sets, Borel and projective filters
Affiliations des auteurs :
Robert Cauty 1 ; Tadeusz Dobrowolski 2 ; Witold Marciszewski 3
@article{10_4064_fm_142_3_269_301,
author = {Robert Cauty and Tadeusz Dobrowolski and Witold Marciszewski},
title = {A contribution to the topological classification of the spaces {{\CYRS}{\cyrr}(X)}},
journal = {Fundamenta Mathematicae},
pages = {269--301},
year = {1993},
volume = {142},
number = {3},
doi = {10.4064/fm-142-3-269-301},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-142-3-269-301/}
}
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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
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