Formally continuous functions on Baire space
Formally continuous functions on Baire space
复制标题
贝尔空间上的形式连续函数
DOI：
10.1002/malq.201700015
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发表时间：
2017
影响因子：
0.3
通讯作者：
Tatsuji Kawai
中科院分区：
文献类型：
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作者：
Tatsuji Kawai
如果一个从贝尔空间NN到自然数N的函数是由相应形式空间之间的态射诱导的，则称为形式连续函数。我们将形式连续性与Bishop构造数学中Baire空间上的另外两个连续性概念进行了比较：一个是由browwer运算诱导的函数（即归纳定义的邻域函数）；另一种是紧像附近一致连续的函数。我们证明了形式连续性与前者是等价的，而它比后者严格地强。形式连续函数与由browwer操作导出的函数的等价性要求可数选择。
A function from Baire space NN to the natural numbers N is called formally continuous if it is induced by a morphism between the corresponding formal spaces. We compare formal continuity to two other notions of continuity on Baire space working in Bishop constructive mathematics: one is a function induced by a Brouwer‐operation (i.e., inductively defined neighbourhood function); the other is a function uniformly continuous near every compact image. We show that formal continuity is equivalent to the former while it is strictly stronger than the latter. The equivalence of formally continuous functions and those induced by Brouwer‐operations requires Countable Choice.