Compact Resolutions and Analyticity

Salvador López-Alfonso, Manuel López-Pellicer () and Santiago Moll-López
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Salvador López-Alfonso: Departamento de Construcciones Arquitectónicas, Universitat Politècnica de València, 46022 Valencia, Spain
Manuel López-Pellicer: Departamento de Matemática Aplicada, IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain
Santiago Moll-López: Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2024, vol. 12, issue 2, 1-7

Abstract: We consider the large class G of locally convex spaces that includes, among others, the classes of ( D F ) -spaces and ( L F ) -spaces. For a space E in class G we have characterized that a subspace Y of ( E , σ ( E , E ′ ) ) , endowed with the induced topology, is analytic if and only if Y has a σ ( E , E ′ ) -compact resolution and is contained in a σ ( E , E ′ ) -separable subset of E . This result is applied to reprove a known important result (due to Cascales and Orihuela) about weak metrizability of weakly compact sets in spaces of class G . The mentioned characterization follows from the following analogous result: The space C ( X ) of continuous real-valued functions on a completely regular Hausdorff space X endowed with a topology ξ stronger or equal than the pointwise topology τ p of C ( X ) is analytic iff ( C ( X ) , ξ ) is separable and is covered by a compact resolution.

Keywords: compact resolution; analytic space; locally convex space; weak metrizability; C p ( X )-spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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