کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4661053 1344398 2007 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Distances from selectors to spaces of Baire one functions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Distances from selectors to spaces of Baire one functions
چکیده انگلیسی

Given a metric space X   and a Banach space (E,‖⋅‖)(E,‖⋅‖) we study distances from the set of selectors Sel(F)Sel(F) of a set-valued map F:X→P(E) to the space B1(X,E)B1(X,E) of Baire one functions from X into E. For this we introduce the d-τ  -semioscillation of a set-valued map with values in a topological space (Y,τ)(Y,τ) also endowed with a metric d. Being more precise we obtain thatd(Sel(F),B1(X,E))⩽2oscw∗(F), where oscw∗(F) is the ‖⋅‖‖⋅‖-w-semioscillation of F. In particular, when F   takes closed values and oscw∗(F)=0 we get that then F has a Baire one selector: we point out that if F   is weakly upper semicontinuous then oscw∗(F)=0 and therefore our results strengthen a Srivatsa selection theorem when F takes closed set. We also obtain similar results when τ is the topology of convergence on some boundary B or τ   is the w∗w∗ topology of a bidual Banach space.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 155, Issue 2, 1 December 2007, Pages 69–81
نویسندگان
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