论文标题
指数矢量空间中的一些特殊集
Some Special Sets in an Exponential Vector Space
论文作者
论文摘要
在本文中，我们研究了“吸收”和“平衡”集合在指数矢量空间（\ emph {evs}简单）上的$ \ mathbb k $的真实或复杂的元素。这些集合起着关键作用来描述拓扑电动汽车的几个方面。我们已经以额外的和吸收套件的拓扑套装来表征了一个添加剂身份的本地基础，该场景是$ \ Mathbb k $。同样，我们发现了一个足够的条件，可以将电动汽车拓扑以形成拓扑电动汽车。接下来，我们在$ \ mathbb k $的拓扑电动汽车中介绍了“有限集”的概念，并在平衡套件的帮助下对它们进行了表征。我们还表明，紧凑性意味着拓扑EV中集合的界限。在最后一部分中，我们介绍了“径向”电动汽车的概念，该电动汽车的特征是$ \ mathbb k $上的电动汽车，直达订单 - 异态。另外，我们已经表明，每个拓扑EVS都是径向的。此外，已经表明，“通常的子空间拓扑是最好的拓扑，$ [0，\ infty）$构成了topological ev，$ \ mathbb k $'topogical EV”。
In this paper, we have studied 'absorbing' and 'balanced' sets in an Exponential Vector Space (\emph{evs} in short) over the field $\mathbb K$ of real or complex. These sets play pivotal role to describe several aspects of a topological evs. We have characterised a local base at the additive identity in terms of balanced and absorbing sets in a topological evs over the field $\mathbb K$. Also, we have found a sufficient condition under which an evs can be topologised to form a topological evs. Next, we have introduced the concept of 'bounded sets' in a topological evs over the field $\mathbb K$ and characterised them with the help of balanced sets. Also we have shown that compactness implies boundedness of a set in a topological evs. In the last section we have introduced the concept of `radial' evs which characterises an evs over the field $\mathbb K$ up to order-isomorphism. Also, we have shown that every topological evs is radial. Further, it has been shown that "the usual subspace topology is the finest topology with respect to which $[0,\infty)$ forms a topological evs over the field $\mathbb K$".
