In mathematics, a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different topologies depending on context, and it may refer to:
- the final topology on the disjoint union
- the topology arising from a norm
- the strong operator topology
- the strong topology (polar topology), which subsumes all topologies above.
Note that a topology τ is stronger than a topology σ (is a finer topology) if τ contains all the open sets of σ.
In algebraic geometry, it usually means the topology of an algebraic variety as complex manifold or subspace of complex projective space, as opposed to the Zariski topology (which is rarely even a Hausdorff space).
Famous quotes containing the word strong:
“... but by that time a lot of sea had rolled by and Lucette was too tired to wait. Then the night was filled with the rattle of an old but still strong helicopter. Its diligent beam could spot only the dark head of Van, who, having been propelled out of the boat when it shied from its own sudden shadow, kept bobbing and bawling the drowned girl’s name in the black, foam-veined, complicated waters.”
—Vladimir Nabokov (1899–1977)