Titlebook: Descriptive Topology in Selected Topics of Functional Analysis; Jerzy Kąkol,Wiesław Kubiś,Manuel López-Pellicer Book 20111st edition Sprin

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泄露

阶层

A Three-Space Property for Analytic Spaces,In this chapter, we show that analyticity is not a three-space property. We prove, however, that a metrizable tvs . is analytic if it contains a complete locally convex analytic subspace . such that the quotient ./. is analytic. We reprove (using Corson’s example) that the Lindelöf property is not a three-space property.

tympanometry

字形刻痕

,Corson’s Property (,) and Tightness,In this chapter, the class of Banach spaces having the property (.) (isolated by Corson) is studied. This property provides a large subclass of Banach spaces . whose weak topology need not be Lindelöf. We collect some results of Corson, Pol, Frankiewicz, Plebanek and Ryll-Nardzewski.

fatuity

Banach Spaces with Many Projections,In this chapter, we discuss Banach spaces that have a rich family of norm-one projections onto separable subspaces. One of the tools, coming from logic, is the concept of an elementary submodel.

Jejune

Cryptic

The Rise of BigTechs in the Financial Market and strong duals of (.)-spaces. We study trans-separable spaces and show that a tvs with a resolution of precompact sets is trans-separable. This is applied to prove that precompact sets are metrizable in any uniform space whose uniformity admits a .-basis.

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