无处连续的Costas函数与无穷Golomb定则
On nowhere continuous Costas functions and infinite Golomb rulers
摘要：
我们证明了无处连续双射满足Costas属性的存在，以及（可数和不可数）无限Golomb统治者。我们定义并证明了存在的真正的和合理的Costas云，即无处连续Costas注入的图形是无处不在的实平面的区域中的密集，基于柯西的函数方程的非线性解决方案。我们还给出了2个无处连续函数的构造性例子，它满足Costas性质的约束形式（仅在有理或代数位移上），基于实数的稠密子集的指示函数。
英文摘要：
We prove the existence of nowhere continuous bijections that satisfy the Costas property, as well as (countably and uncountably) infinite Golomb rulers. We define and prove the existence of real and rational Costas clouds, namely nowhere continuous Costas injections whose graphs are everywhere dense in a region of the real plane, based on nonlinear solutions of Cauchy's functional equation. We also give 2 constructive examples of a nowhere continuous function, that satisfies a constrained form of the Costas property (over rational or algebraic displacements only, that is), based on the indicator function of a dense subset of the reals.
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