杨毅;鲍猛;徐晓泉;

• 1:闽南师范大学数学与统计学院
• 2:四川大学数学学院

摘要(Abstract)：

主要讨论k-有界sober空间对遗传、收缩、函数空间和Smyth幂构造的封闭性,证明了k-有界sober空间是饱和遗传的,但不是闭遗传的;对收缩与Smyth幂构造均不具有封闭性.还证明了存在k-有界sober空间X使得函数空间[X→X]赋予点式收敛拓扑不是k-有界sober空间.

关键词(KeyWords)： k-有界sober空间;遗传性;收缩;函数空间;Smyth幂空间

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(12071199,11661057);; 江西省自然科学基金(20192ACBL20045)

作者(Authors): 杨毅;鲍猛;徐晓泉;

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