Normed Space에서 Topology들의 비교

Abstract

A normed space is a metric space, and, as such, it is a topological space. The metric topology(or norm topology) is often called the strong topology. Another topology, called the weak topology, plays an important role in the theory of normed spaces. If more than one topology is considered, then the relations of the topologies to one another must be clarified. In this paper we clarify the relations of following properties; finite dimensionality, closure, convergence, compact.