论文标题
$ l $ - 反应
$L$-retracts
论文作者
论文摘要
我们研究了$ l $等价性的关系，该关系源自自由局部凸空间的构建，这是一个概念，该概念具体概念了与连续函数的同时扩展有关的几个概念。我们还探讨了这个概念与Dugundji的扩展定理的关系，并且基于该定理，我们提供了足够的条件，使我们能够在不同类型的拓扑空间中识别这些集合。特别是，我们提出了一种构建$ l $等效映射示例（以及$ l $ - 等效空间）的方法，该方法表明，开放或封闭映射的属性不是$ l $ invariant。
We study the relation of $L$-equivalence, which derives from the construction of the free locally convex spaces, through a concept that particularizes several notions related to the simultaneous extension of continuous functions. We also explore the relationship that this concept has with the Dugundji's extension theorem, and, based on this theorem we give sufficient conditions that allow us to identify these sets in different types of topological spaces. In particular, we present a method for constructing examples of $L$-equivalent mappings (and hence $L$-equivalent spaces) that show that the properties of being an open or closed mapping are not $L$-invariant.
