标题： 有序紧集的维托里斯拓扑的适应 显示英文标题

标题： An Adaptation of the Vietoris Topology for Ordered Compact Sets

摘要： 我们在一个空间的幂上引入了一种自然拓扑，这种拓扑受到紧子集上的Vietoris拓扑的启发。 然后我们将这种拓扑与其他乘积拓扑进行比较；具体来说，我们将其与Tychonoff乘积、方体乘积和Bell的均匀方体拓扑进行比较。 我们确定了当基础空间是离散空间时的各种拓扑性质。 当基础空间是欧几里得实数线时，我们证明所得的幂不是Lindelöf的，因此也不是Menger的。 这表明，与无序紧子集上的Vietoris拓扑不同，基础空间的覆盖性质不一定传递到Vietoris幂上。 显示英文摘要

摘要： We introduce a natural topology on powers of a space that is inspired by the Vietoris topology on compact subsets. We then place this topology in context with other product topologies; specifically, we compare this topology with the Tychonoff product, the box product, and Bell's uniform box topology. We identify a variety of topological properties for the specific case when the ground space is discrete. When the ground space is the Euclidean real line, we show that the resulting power is not Lindel\"{o}f, and hence, not Menger. This shows that, unlike the the Vietoris topology on unordered compact subsets, covering properties of the ground space need not transfer to the Vietoris power.