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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Generalized limits of affine functions
 Holub, Aleš ; Spurný, Jiří (advisor) ; Holický, Petr (referee)
We construct a co-analytic filter on the set of finite sequences of natural numbers, which allows us to obtain a strongly affine function of arbitrary Borel class from compact convex subset of locally convex space through single limit process (by this filter) applied to countable system of affine continuous functions. Conversely we show that function obtainted as result of such process is necessarily Borel and strongly affine. Further we generalize this method using metrizable reduction approach for Baire functions on non-metrizable spaces. Last chapter covers similar result for bi-analytic functions on separable metrizable spaces.
Detailed record
Generalized limits of affine functions
 Holub, Aleš ; Spurný, Jiří (advisor) ; Holický, Petr (referee)
We construct a co-analytic filter on the set of finite sequences of natural numbers, which allows us to obtain a strongly affine function of arbitrary Borel class from compact convex subset of locally convex space through single limit process (by this filter) applied to countable system of affine continuous functions. Conversely we show that function obtainted as result of such process is necessarily Borel and strongly affine. Further we generalize this method using metrizable reduction approach for Baire functions on non-metrizable spaces. Last chapter covers similar result for bi-analytic functions on separable metrizable spaces.
Detailed record

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