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Math and science::Topology

Finer and coarser topologies

We say that one topology T on X is finer than another topology T on X iff [in words...]. T is said to be coarser than T.

Stronger and weaker are alternative terminology for finer and coarser.

T is strictly finer iff [...]

Symbolically,

  • T is finer than T[...].
  • T is strictly finer than T[...].