Affine extensions of functions with a closed graph

Wójtowicz, Marek; Sieg, Waldemar

doi:10.7494/opmath.2015.35.6.973

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Note That For X An Isolated Point We May Set1

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Cited by 4 publications

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“…From (17) and (22) we get (21). Moreover (since Wj ⊂ Wj+1 for every j ∈ N), we also have y / ∈ Wj for j k0.…”

Section: Note That For X An Isolated Point We May Setmentioning

confidence: 90%

Linear extensions of some Baire-one functions

Sieg

2017

Arch. Math.

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Let X be a Hausdorff topological space, and let B1(X) denote the space of all real Baire-one functions defined on X. Let A be a nonempty subset of X endowed with the topology induced from X, and let F(A) be the set of functions A → R with a property F making F(A) a linear subspace of B1(A). We give a sufficient condition for the existence of a linear extension operator TA : F(A) → F(X), where F means to be piecewise continuous on a sequence of closed and G δ subsets of X and is denoted by P0. We show that TA restricted to bounded elements of F(A) endowed with the supremum norm is an isometry. As a consequence of our main theorem, we formulate the conclusion about existence of a linear extension operator for the classes of Baire-one-star and piecewise continuous functions.

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“…From (17) and (22) we get (21). Moreover (since Wj ⊂ Wj+1 for every j ∈ N), we also have y / ∈ Wj for j k0.…”

Section: Note That For X An Isolated Point We May Setmentioning

confidence: 90%