Le degré de Lindelöf est $l$-invariant.

Ahmed Bouziad (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

The Lindelöf number $l(X)$ of a Tychonoff space $X$ is the smallest infinite cardinal $\tau$ such that any open cover of $X$ contains a subcover of cardinality less than or equal to $\tau$. The symbol $C_p(X)$ denotes the space of real-valued continuous functions on $X$ endowed with the topology of simple convergence. A well known fact is that if $C_p(X)$ and $C_p(Y)$ are isomorphic as topological rings, then $X$ and $Y$ are homeomorphic. The main resul of this paper shows that if $C_p(X)$ and $C_p(Y)$ are linearly homeomorphic, then $l(X)=l(Y)$.

Mots clés: Lindelof number; linearly hompeomorphic spaces; space of continuous functions; pointwise convergence topology

Domaines: Topologie générale [math.GN]

Ahmed Bouziad. Le degré de Lindelöf est $l$-invariant.. Proceedings of the American Mathematical Society, 2001, 129 (3), pp.913--919. ⟨hal-00373441⟩