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设X=[0,1],T是一个有限树，文章定义了从X到T的连续函数空间↓C(X,T).对于T中的一个枝S，文献[1]中研究了最大元在S上的连续函数空间↓C(X,T)的子集CUB(S)及其闭包AUB(S)的拓扑结构，但是AUB(S)的定义看上去并不是那么地自然.文章用下方图形定义了AUB(S)的子集AUB'(S)，主要的结果是：构造了一个连续映射vb~A:[0,b]→AUB(S)使得vb~A(0)=A且vb~A(c)∈AUB(S)，进一步当c>0时有vb~A(c)∈AUB'(S)，其中b∈[0,1),c∈[0,b],A∈AUB(S).
Abstract：For X=[0,1], T is a finite tree. The continuous functions space↓C(X,T) from X to T is defined. For a segment S of finite tree T, the subset CUB(S)of the space ↓C(X,T) of continuous functions on S with the maximum value and its closure AUB(S)'s topological structure is investigated in [2], but the definition of AUB(S) does not look so natural. In this paper, the subset AUB'(S)of AUB(S) with hypographs is defined. The main results are: a continuous map vb~A: [0,b] → AUB(S) is established and v_ε(0)=A, vb~A(c)∈AUB'(S), where c∈[0,b].
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基本信息:
中图分类号:O189
引用信息:
[1]董凯宏,杨寒彪.值域为有限树的函数空间的拓扑性质[J].汕头大学学报(自然科学版),2026,41(01):65-70.
基金信息:
国家自然科学基金青年项目C类（12201470）; 广东省自然科学基金面上项目（2023A1515010819）
2026-02-15
2026-02-15