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:
““The unities, sir,’ he said, “are a completeness—a kind of universal dovetailedness with regard to place and time—a sort of general oneness, if I may be allowed to use so strong an expression. I take those to be the dramatic unities, so far as I have been enabled to bestow attention upon them, and I have read much upon the subject, and thought much.””
—Charles Dickens (1812–1870)