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Distinguished Cp (X) spaces and the strongest locally convex topology


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Título :
Distinguished Cp (X) spaces and the strongest locally convex topology
Autor :
Ferrando, Juan Carlos  
Saxon, Stephen  
Editor :
Springer
Departamento:
Departamentos de la UMH::Estadística, Matemáticas e Informática
Fecha de publicación:
2023-08
URI :
https://hdl.handle.net/11000/30590
Resumen :
Since Tychonoff spaces X serve as continuous Hamel bases for the strong dual Lβ (X) of Cp (X), an old splitting theorem proves: Cp (X) is distinguished ⇔ Lβ (X) has the strongest locally convex topology (slctop) [Ferrando/Ka˛kol]. Our new splitting theorem: The span LX (Y ) of Y ⊆ X complements LX (X\Y ) in Lβ (X). Thereby we prove If X = Y1 ∪· · ·∪Yn and each Cp Yj is distinguished, then so is Cp (X), provided either (i) all Yj are Gδ sets, or (ii) all are Fσ sets. Hence, provided (iii) all Yj are open, or (iv) all are closed. Parts (ii)/(iv) extend to countable unions (known). Part (i) does not, via Michael’s line. Countable case (iii) remains open. A dozen recent related results are proved/improved in our slctop analysis of Lβ (X).
Palabras clave/Materias:
Distinguished
Barrelled
ϕ-complemental
Stationary sets
Bidual
∑(X)
Área de conocimiento :
CDU: Ciencias puras y naturales: Matemáticas
Tipo documento :
application/pdf
Derechos de acceso:
info:eu-repo/semantics/closedAccess
DOI :
https://doi.org/10.1007/s13398-023-01498-4
Aparece en las colecciones:
Artículos Estadística, Matemáticas e Informática



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