- Tytuł:
- A contribution to the topological classification of the spaces Ср(X)
- Autorzy:
-
Cauty, Robert
Dobrowolski, Tadeusz
Marciszewski, Witold - Powiązania:
- https://bibliotekanauki.pl/articles/1208632.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
function space
pointwise convergence topology
absorbing sets
Borel and projective filters - Opis:
- 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 $Ω_α$.
- Źródło:
-
Fundamenta Mathematicae; 1993, 142, 3; 269-301
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł