A hierarchy in the family of real surjective functions
A hierarchy in the family of real surjective functions
复制标题
实满射函数族中的层次结构
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
E. Sáez
中科院分区：
文献类型：
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作者：
Mar Fenoy;José L. Gámez;G. A. Muñoz;E. Sáez
摘要：本文主要研究了一类极值满射函数。我们通过举例和关键性质给出了几种不同类型的极端满射。这些例子帮助我们在我们处理的不同类的满性中建立一个层次结构。这里介绍的类有：处处满射函数，强处处满射函数，κ处处满射函数，完全处处满射函数和琼斯函数。本文用线性的概念研究了满射函数集的代数结构。在这项工作的最后部分，我们还揭示了上述不同程度的极限满射与其他有趣的函数集之间的意想不到的联系，如加性映射空间，具有密集图的映射类，达布函数类和Sierpiński-Zygmund函数类。
Abstract This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The algebraic structure of the sets of surjective functions we show here is studied using the concept of lineability. In the final sections of this work we also reveal unexpected connections between the different degrees of extreme surjectivity given above and other interesting sets of functions such as the space of additive mappings, the class of mappings with a dense graph, the class of Darboux functions and the class of Sierpiński-Zygmund functions in ℝℝ.