On the functor of comonotonically maxitive functionals

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-11-05 DOI:10.1016/j.topol.2024.109131

Taras Radul

引用次数: 0

Abstract

We introduce a functor of functionals that preserve the maximum of comonotone functions and the addition of constants. This functor is a subfunctor of the functor of order-preserving functionals and includes the idempotent measure functor as a subfunctor. The main aim of this paper is to demonstrate that this functor is isomorphic to the capacity functor. We establish this isomorphism using the fuzzy max-plus integral. In essence, this result can be viewed as an idempotent analogue of the Riesz Theorem, which establishes a correspondence between the set of σ-additive regular Borel measures and the set of positive linear functionals.

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论最大单调函数的函子

我们引入了一个保留协和函数最大值和常量加法的函数函子。这个函子是保阶函数函子的一个子函子，包括作为子函子的幂等度量函子。本文的主要目的是证明这个函子与容量函子同构。我们利用模糊最大加积分建立了这种同构性。从本质上讲，这一结果可以看作是 Riesz 定理的empotent 类似物，它在 σ-additive regular Borel 测量集合和正线性函数集合之间建立了对应关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.