当前位置: X-MOL 学术Results Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Additivity Coefficients for all Classes in the Algebra of Darboux-Like Maps on $$\mathbb {R}$$ R
Results in Mathematics ( IF 2.2 ) Pub Date : 2020-12-23 , DOI: 10.1007/s00025-020-01287-0
K. C. Ciesielski , T. Natkaniec , D. L. Rodríguez-Vidanes , J. B. Seoane-Sepúlveda

The class \(\mathbb D\) of generalized continuous functions on \(\mathbb {R}\) known under the common name of Darboux-like functions is usually described as consisting of eight families of maps: Darboux, connectivity, almost continuous, extendable, peripherally continuous, those having perfect road, and having either the Cantor Intermediate Value Property or the Strong Cantor Intermediate Value Property. The algebra \(\mathcal {A}(\mathbb D)\) of classes of functions generated by these families contains 17 atoms. In this work we will calculate the values of the additivity coefficient \({{\,\mathrm{A}\,}}(\mathcal {F})\) for all atoms \(\mathcal {F}\) in the algebra \(\mathcal {A}(\mathbb D)\). We also determine the values \({{\,\mathrm{A}\,}}(\mathcal {F})\) for a lot of other families \(\mathcal {F}\in \mathcal {A}(\mathbb D)\). Open questions and new directions of research shall also be provided.



中文翻译:

$$ \ mathbb {R} $$ R上达布克斯式地图的代数中所有类的加和系数

\(\ mathbb d \)的广义的连续函数\(\ mathbb {R} \)下的通用名已知达布样功能通常被描述为包括8个家庭的地图的:达布,连通性,几乎连续的,可扩展,周边连续,具有完美道路并具有Cantor中值属性或Strong Cantor中值属性的对象。这些族生成的函数的代数\(\ mathcal {A}(\ mathbb D)\)包含17个原子。在这项工作中,我们将计算原子中所有原子\(\ mathcal {F})的加和系数\({{\,\ mathrm {A} \,}}(\ mathcal {F})\)的值。代数\(\ mathcal {A}(\ mathbb D)\)。我们还为\ mathcal {A}(中的其他许多族\(\ mathcal {F} \ \ mathbb D)\)。还应提供开放的问题和新的研究方向。

更新日期:2020-12-23
down
wechat
bug