Skip to main content
1 of 1
Post Made Community Wiki
Jon Bannon
  • 7.1k
  • 6
  • 69
  • 112

Functional analysis, and in particular the theory of operator algebras, involves many such topologies. For example, neither the strong operator nor the weak operator topology on $B(H)$, the algebra of bounded operators on a separable Hilbert space $H$ is metrizable (but give metrizable topologies when restricted to bounded sets). See the Wikipedia article for more such examples.

Jon Bannon
  • 7.1k
  • 6
  • 69
  • 112