拓扑向量空间上的Peano曲线
Peano curves on topological vector spaces
摘要：
本文的出发点是Peano曲线的存在性，即单位区间映射到单位平方上的连续满射。从这个事实，人们可以很容易地构造出从实数线$\mathbb{R}$到任何欧几里得空间$\mathbb{R}^n$的连续满射。代数结构的一组这些功能（以及扩展到空间与更高的维度）进行了分析，从现代的角度来看，线性，和大代数的家庭内发现的研究。我们还研究了拓扑向量空间的连续图像的实直线，提供了一个最佳的线性化结果。
英文摘要：
The starting point of this paper is the existence of Peano curves, that is, continuous surjections mapping the unit interval onto the unit square. From this fact one can easily construct of a continuous surjection from the real line $\mathbb{R}$ to any Euclidean space $\mathbb{R}^n$. The algebraic structure of the set of these functions (as well as extensions to spaces with higher dimensions) is analyzed from the modern point of view of lineability, and large algebras are found within the families studied. We also investigate topological vector spaces that are continuous image of the real line, providing an optimal lineability result.
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