论文标题
延长本地凸空间的最优质的本地凸拓扑
The finest locally convex topology of an extended locally convex space
论文作者
论文摘要
萨拉斯（Salas）和加西亚（Garcia）在[D.萨拉斯和S. tapia-garcia。扩展的静态和扩展的拓扑矢量空间。拓扑及其应用，2016年]，扩展了扩展规范空间的想法（Beer在G. Beer。具有无限价值的规范中引入。本文提供了局部凸出空间的最优质局部凸拓扑的有吸引力的表述，并对所得局部凸出空间进行了系统的研究。作为一种应用，我们表征了对应于功能空间C（x）的Bornology上均匀和强统一收敛拓扑的最优质局部凸拓扑的巧合。
Salas and Garcia introduced the concept of an extended locally convex space in [D. Salas and S. Tapia-Garcia. Extended seminorms and extended topological vector spaces. Topology and its Applications, 2016] which extends the idea of an extended normed space (introduced by Beer in G. Beer. Norms with infinite values. Journal of Convex Analysis, 2015). This article gives an attractive formulation of the finest locally convex topology of an extended locally convex space and provides a systematic study of the resulting locally convex space. As an application, we characterize the coincidence of the finest locally convex topologies corresponding to the topologies of uniform and strong uniform convergences on a bornology for the function space C(X).
