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The controlled separable projection property for Banach spaces

Jesús FerrerMarek Wójtowicz — 2011

Open Mathematics

Let X, Y be two Banach spaces. We say that Y is a quasi-quotient of X if there is a continuous operator R: X → Y such that its range, R(X), is dense in Y. Let X be a nonseparable Banach space, and let U, W be closed subspaces of X and Y, respectively. We prove that if X has the Controlled Separable Projection Property (CSPP) (this is a weaker notion than the WCG property) and Y is a quasi-quotient of X, then the structure of Y resembles the structure of a separable Banach space: (a) Y/W is norm-separable...

On a class of real normed lattices

C. AlegreJesús FerrerValentín Gregori — 1998

Czechoslovak Mathematical Journal

We say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that E is a quasi-Baire space iff ( E , T ( 𝒰 ) , T ( 𝒰 - 1 ) ) , is a pairwise Baire bitopological space, where 𝒰 , is a quasi-uniformity that determines, in L . Nachbin’s sense, the topological ordered space E .

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