Editing Weak topology (section)

=== Other properties ===

If {{mvar|X}} is equipped with the weak topology, then addition and scalar multiplication remain continuous operations, and {{mvar|X}} is a [[locally convex topological vector space]].

If {{mvar|X}} is a normed space, then the dual space <math>X^*</math> is itself a normed vector space by using the norm

:<math>\|\phi\|=\sup_{\|x\|\le 1} |\phi(x)|.</math>

This norm gives rise to a topology, called the '''strong topology''', on <math>X^*</math>. This is the topology of [[uniform convergence]]. The uniform and strong topologies are generally different for other spaces of linear maps; see below.