Editing Comparison of topologies (section)

== Examples ==

The finest topology on ''X'' is the [[discrete topology]]; this topology makes all subsets open.  The coarsest topology on ''X'' is the [[trivial topology]]; this topology only admits the empty set
and the whole space as open sets.

In [[function space]]s and spaces of [[Measure (mathematics)|measures]] there are often a number of possible topologies. See [[topologies on the set of operators on a Hilbert space]] for some intricate relationships.

All possible [[polar topology|polar topologies]] on a [[dual pair]] are finer than the [[weak topology (polar topology)|weak topology]] and coarser than the [[strong topology (polar topology)|strong topology]].

The [[Complex coordinate space|complex vector space]] '''C'''<sup>''n''</sup> may be equipped with either its usual (Euclidean) topology, or its [[Zariski topology]]. In the latter, a subset ''V'' of '''C'''<sup>''n''</sup> is closed if and only if it consists of all solutions to some system of polynomial equations. Since any such ''V'' also is a closed set in the ordinary sense, but not ''vice versa'', the Zariski topology is strictly weaker than the ordinary one.