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A hierarchy in the family of real surjective functions

100%

Fenoy-Muñoz M., Gámez-Merino J. L., Muñoz-Fernández G. A., Sáez-Maestro E.

Open Mathematics

2017

tom 15

nr 1

486-501

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.

An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem

100%

Oertel F.

Dependence Modeling

2015

tom 3

nr 1

We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.

Ograniczanie wyników

1 Dependence Modeling

1 Open Mathematics

1 Fenoy-Muñoz M.

1 Gámez-Merino J. L.

1 Muñoz-Fernández G. A.

1 Oertel F.

1 Sáez-Maestro E.

1 2017

1 2015

Wyniki wyszukiwania

A hierarchy in the family of real surjective functions

An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem