1. Le degré de Lindelöf est $l$-invariant
- Author
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Ahmed Bouziad, Laboratoire de Mathématiques Raphaël Salem (LMRS), Université de Rouen Normandie (UNIROUEN), and Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Discrete mathematics ,linearly hompeomorphic spaces ,Function space ,Applied Mathematics ,General Mathematics ,Tychonoff space ,Mathematics::Number Theory ,010102 general mathematics ,pointwise convergence topology ,Mathematics::General Topology ,16. Peace & justice ,01 natural sciences ,010101 applied mathematics ,[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN] ,space of continuous functions ,Lindelof number ,0101 mathematics ,Mathematics - Abstract
International audience; 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 $l(X)=l(Y)$.
- Published
- 2001