<P> The group of unitary operators U (H) (\ displaystyle \ mathbb (U) ((\ mathcal (H)))) on a separable Hilbert space H (\ displaystyle (\ mathcal (H))) endowed with the strong operator topology is metrizable (see Proposition II. 1 in). </P> <P> Non-normal spaces cannot be metrizable; important examples include </P> <Ul> <Li> the Zariski topology on an algebraic variety or on the spectrum of a ring, used in algebraic geometry, </Li> <Li> the topological vector space of all functions from the real line R to itself, with the topology of pointwise convergence . </Li> </Ul> <Li> the Zariski topology on an algebraic variety or on the spectrum of a ring, used in algebraic geometry, </Li>

Give an example of a topological space which is not metrizable