TUBES ABOUT FUNCTIONS AND MULTIFUNCTION

Gerald Beer; Michael J. Hoffman

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TUBES ABOUT FUNCTIONS AND MULTIFUNCTION

机译：关于功能和多功能的管

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We provide a characterization of lower semicontinuity for multifunctions with values in a metric space 〈Y,d〉 which, in the special case of single-valued functions, says that a function is continuous if and only if for each ε＞0, the ε-tube about its graph is an open set. Applications are given, one of which provides a novel understanding of the Open Mapping Theorem from functional analysis. We also give a related but more complicated characterization of upper semicontinuity for multifunctions with closed values in a metrizable space.

机译：我们提供了度量空间为的多元函数的下半连续性的表征，在单值函数的特殊情况下，当且仅当每个ε＞ 0时，ε才是连续的其图的-tube是一个开放集。给出了应用程序，其中之一提供了从功能分析对开放映射定理的新颖理解。我们还给出了一个可积空间中具有闭合值的多功能的上半连续性的相关但更复杂的刻画。

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来源
《Real analysis exchange》 |2014年第1期|33-43|共11页
作者
Gerald Beer; Michael J. Hoffman;
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作者单位

Department of Mathematics, California State University Los Angeles, 5151 State University Drive, Los Angeles, California 90032, USA;

Department of Mathematics, California State University Los Angeles, 5151 State University Drive, Los Angeles, California 90032,USA;

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原文格式 PDF
正文语种 eng
中图分类
关键词
tube; semicontinuous multifunction; semicontinuous function; continuous function; uniform convergence; open mapping; Open Mapping Theorem;

机译：管;半连续多功能半连续函数连续功能统一收敛;开放地图;开放映射定理;

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1. Contractive multifunctions, fixed point inclusions and iterated multifunction systems [J] . H.E. Kunze, D. La Torre, E.R. Vrscay Journal of Mathematical Analysis and Applications . 2007,第1期

机译：压缩多功能，定点包含和迭代多功能系统
2. Multifunctions determined by integrable functions [J] . Candeloro Domenico, Di Piazza Luisa, Musial Kazimierz, Acoustic bulletin . 2019,第SEPa期

机译：由可积函数确定的多功能
3. Noninvasive Detection of Functional Myocardial Ischemia: Multifunction Cardiogram Evaluation in Diagnosis of Functional Coronary Ischemia Study (MED-FIT) [J] . Kawaji Tetsuma, Shiomi Hiroki, Morimoto Takeshi, Annals of noninvasive electrocardiology: the official journal of the International Society for Holter and Noninvasive Electrocardiology, Inc . 2015,第5期

机译：功能性心肌缺血的无创检测：多功能心电图评估功能性冠状动脉缺血性研究的研究（MED-FIT）
4. The multifunction traveling-wave tube: A versatile microwave component for military systems [C] . Hodowanec C., Wolkstein H.J., McMurrough R., Electron Devices Meeting, 1965 International . -1

机译：多功能行波管：用于军事系统的多功能微波组件
5. The nonexistence of shearlet-like scaling multifunctions that satisfy certain minimally desirable properties and characterizations of the reproducing properties of the integer lattice translations of a countable collection of square integrable functions [D] . Houska, Robert Timothy 2009

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6. Noninvasive Detection of Functional Myocardial Ischemia: Multifunction Cardiogram Evaluation in Diagnosis of Functional Coronary Ischemia Study (MED‐FIT) [O] . Tetsuma Kawaji, Hiroki Shiomi, Takeshi Morimoto, 2015

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7. High level measurement comparison on a high performance multifunction calibrator between THE INRIM-Lab for multifunction instruments calibration and an Accredited Electrical Calibration Laboratory [O] . F.Galliana, M. Lanzillotti and G. La Paglia 2015

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TUBES ABOUT FUNCTIONS AND MULTIFUNCTION

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