An approximative generalization of Zahorski's theorem on derivative

H. H. Pu; H. W. Pu

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Baire spaces

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CONTENTSIntroduction............................................................................................................ 5I. Basic properties of Baire spaces................................................................... 61. Nowhere dense sets............................................................................................... 62. First and second category sets............................................................................. 83. Baire spaces................................................................................................................

Maximal additive and maximal multiplicative family for the family of $ℬ$ -Darboux Baire one functions

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On the prolongation of restrictions of Baire 1 functions to functions which are quasicontinuous and approximately continuous

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Let I ⊂ ℝ be an open interval and let A ⊂ I be any set. Every Baire 1 function f: I → ℝ coincides on A with a function g: I → ℝ which is simultaneously approximately continuous and quasicontinuous if and only if the set A is nowhere dense and of Lebesgue measure zero.

On topological properties of the spaces of Darboux Baire 1 functions and bounded derivatives

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We investigate the topological structure of the space 𝓓ℬ₁ of bounded Darboux Baire 1 functions on [0,1] with the metric of uniform convergence and with the p*-topology. We also investigate some properties of the set Δ of bounded derivatives.