A generalization of a Baire theorem concerning barely continuous functions

Karlova Olena

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A generalization of a Baire theorem concerning barely continuous functions

机译：关于几乎没有连续功能的Baire定理的概括

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We prove that if X is a paracompact space, Y is a metric space and f : X - Y is a functionally fragmented map, then (i) f is sigma-discrete and functionally F-sigma-measurable; (ii) f is a Baire-one function, if Y is weak adhesive and weak locally adhesive for X; (iii) f is countably functionally fragmented, if X is Lindeloff. This result generalizes one theorem of Rene Baire on classification of barely continuous functions. (C) 2019 Elsevier B.V. All rights reserved.

机译：我们证明，如果x是Paracompact空间，则Y是度量空间，F：X - > Y是一个功能碎片化的地图，那么（i）f是Sigma离散且功能上的F-Sigma可测量; （ii）F是一个拜尔 - 一种功能，如果Y是弱粘合剂和弱局部粘合剂，则X; （iii）f是可以在功能上碎片化的，如果x是lindeloff。该结果推广了RENE BAIRE的一个定理对勉强连续功能的分类。（c）2019 Elsevier B.v.保留所有权利。

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来源
《Topology and its applications》 |2019年第may15期|433-438|共6页
作者
Karlova Olena;
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作者单位

Jan Kochanowski Univ Humanities & Sci Kielce Poland|Yurii Fedkovych Chernivtsi Natl Univ Chernovtsy Ukraine;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Fragmented function; Baire-one function; F-sigma-measurable function; sigma-Discrete function;

机译：碎片功能;Baire-One功能;F-Sigma可测量的功能;Sigma离散功能;

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专利

1. A generalization of a Baire theorem concerning barely continuous functions [J] . Karlova Olena Topology and its applications . 2019,第MAYa15期

机译：关于几乎连续函数的Baire定理的推广
2. SET-VALUED GENERALIZATIONS OF BAIRES CATEGORY THEOREM [J] . Urbaniec P. Journal of Mathematical Analysis and Applications . 1995,第3期

机译：Baires类别定理的设定值广义
3. Note on a generalization of a theorem of Baire [J] . Chittenden E. W. Bulletin of the American Mathematical Society . 1920,第1期

机译：关于Baire定理的一般化的注记
4. Generalizations of the Intermediate Value Theorem for Approximating Fixed Points and Zeros of Continuous Functions [C] . Michael N. Vrahatis International conference on mumerical computations: theory and algorithms . 2019

机译：逼近连续点的不动点和零点的中间值定理的一般化
5. The Baire category theorem: Its scope. [D] . Jones, Sara Hawtrey. 1995

机译：贝儿类别定理：其范围。
6. A GENERALIZATION OF WHITNEYS THEOREM ON IDEALS OF DIFFERENTIABLE FUNCTIONS [O] . Leopoldo Nachbin 1957

机译：关于微分函数理想的惠特尼定理的推广
7. Generalizations of a theorem of Sarkovskii on orbits of continuous real-valued functions [O] . Baldwin Stewart 1987

机译：连续实值函数轨道上的Sarkovskii定理的推广

A generalization of a Baire theorem concerning barely continuous functions

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