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Distinguished Cp (X) spaces and the strongest locally convex topology
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Title: Distinguished Cp (X) spaces and the strongest locally convex topology |
Authors: Ferrando, Juan Carlos ![](/jspui/image/ORCID.jpg) Saxon, Stephen ![](/jspui/image/ORCID.jpg) |
Editor: Springer |
Department: Departamentos de la UMH::Estadística, Matemáticas e Informática |
Issue Date: 2023-08 |
URI: https://hdl.handle.net/11000/30590 |
Abstract:
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).
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Keywords/Subjects: Distinguished Barrelled ϕ-complemental Stationary sets Bidual ∑(X) |
Knowledge area: CDU: Ciencias puras y naturales: Matemáticas |
Type of document: application/pdf |
Access rights: info:eu-repo/semantics/closedAccess |
DOI: https://doi.org/10.1007/s13398-023-01498-4 |
Appears in Collections: Artículos Estadística, Matemáticas e Informática
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