Preference orders and continuous representations

Mathematica Slovaca

Rita Ceppitelli¹  Ghanshyam Mehta¹  Alessandro Caterino¹ 

关键词: preordered topological space;    representation theorems;    netweight;   

DOI  :  10.2478/s12175-010-0062-2

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.

【 授权许可】

Unknown