低密度软运算符和密度软拓.
Zanyar A Ameen1, Mesfer H Alqahtani2, Ohud F Alghamdi3
1Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq.
Heliyon
|December 17, 2024
概括
本研究介绍了抽象可充电软空间上的低密度软运算符和密度软拓. 它确立了这些运算符生成参数系统并导致拓,其中Borel软西格玛代数与Baire属性软集对齐.
科学领域:
- 拓学的拓学
- 集合理论 集合理论
- 测量理论 测量理论
背景情况:
- 经典密度拓依赖于可测集的莱贝斯格密度点.
- 威尔斯基将密度点的定义概括起来,在类别和量度理论上都证明了它的有效性.
- 密度点集需要较低密度操作者的特定属性.
研究的目的:
- 在抽象可充电软空间上引入和分析低密度软运算符.
- 为了研究由这些运算符生成的密度软拓的特性.
- 描述软密度拓及其与贝尔特征的关系.
主要方法:
- 定义和探索低密度软操作员的基本特性.
- 证明每个低密度软运算符定义了一个参数低密度运算符系统.
- 分析这些运算符生成的密度软拓的拓性质.
主要成果:
- 介绍低密度软操作员及其基本特征.
- 从单一运营商中建立参数低密度运营商的生成.
- 密度软拓的表征,包括波雷尔软西格玛代数和软集软西格玛代数与贝尔属性的等价.
结论:
- 低密度软运算符为构建新的软拓提供了一个框架.
- 密度软拓表现出显著的拓性质,扩展了古典概念.
- 一个关键的发现是Borel软西格玛代数和Baire属性软集在这些拓中的巧合.
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