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Le degré de Lindelöf est $l$-invariant
- Source :
- Proceedings of the American Mathematical Society, Proceedings of the American Mathematical Society, American Mathematical Society, 2001, 129 (3), pp.913--919
- Publication Year :
- 2001
- Publisher :
- HAL CCSD, 2001.
-
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 $l(X)=l(Y)$.
- 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
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[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]
space of continuous functions
Lindelof number
0101 mathematics
Mathematics
Subjects
Details
- Language :
- French
- ISSN :
- 00029939 and 10886826
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society, Proceedings of the American Mathematical Society, American Mathematical Society, 2001, 129 (3), pp.913--919
- Accession number :
- edsair.doi.dedup.....d11ecd35c23cc2cfa8ad4fd8590c307c