一句话：提出强联合允许性概念，并给出递归函数、连续函数及有效拓扑可计算情形下局部性质扩展到并集的充要/充分条件。
论文研究函数类在“局部—整体”上的拼接问题：给定函数类与有限个集合，判断该类是否包含一个函数，其定义域位于这些集合的并集之内，且在每个集合上的限制都属于该类；满足此性质的集合族称为对该类强联合允许（join permitting 则去掉“子集”条件）。作者针对三类情形证明定理：一是潜在部分递归函数类与自然数 n 元组集合族，给出强联合允许的充要条件；二是两个拓扑空间之间的连续部分函数类，给出充分条件，并在对第二个空间的弱假设下证明必要性；三是有效拓扑空间中可计算性的类似结果。评估为数学证明，未涉及实现或实验。
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to all of them belong to this class. The collections with the formulated property are said to be strongly join permitting for the given class (the notion of join permitting collection is defined in the same way, but without the words "a subset of"). Three theorems concerning certain instances of the problem are proved. A necessary and sufficient condition for being strongly join permitting is given for the case when, for some $n$, the class consists of the potentially partial recursive functions of $n$ variables, and the collection consists of sets of $n$-tuples of natural numbers. The second theorem gives a sufficient condition for the case when the class consists of the continuous partial functions between two given topological spaces, and the collection consists of subsets of the first of them (the condition is also necessary under a weak assumption on the second one). The third theorem is of a similar character but, instead of continuity, it concerns computability in the spirit of the one in effective topological spaces.
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@article{Skordev16,
title = {Some theorems on passing from local to global presence of properties of functions},
author = {Dimiter Skordev},
journal = {Logical Methods in Computer Science},
volume = {Volume 12, Issue 4},
year = {2017},
doi = {10.2168/lmcs-12(4:3)2016}
}