Talk:Final topology

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[edit] Coarsest topology

I'm removing the following from the article:

• Given a family of topologies {τ_i} on a fixed set X the final topology on X with respect to the functions id_X : (X, τ_i) → X is the infimum (or meet) of the topologies {τ_i} in the lattice of topologies on X. That is, the final topology τ is the intersection of the topologies {τ_i}.

I beleive this one is supposed to describe the initial topology not the final topology: The intersection of two topologies will be coarser or weaker than any of the individual τ_i. Elsewhere, the article describes the final topology as being the "finest" not the "coarsest".

I'll be removing a similar paragraph from the initial topology article. linas 20:14, 20 November 2005 (UTC)

Be careful Linas; the example is correct. You are confusing greatest element with greatest lower bound. The topology on X must be coarser than each given topology to ensure continuity (i.e. a lower bound), but it is the finest topology which is coarser than each given one (i.e. a greatest lower bound). -- Fropuff 16:15, 21 November 2005 (UTC)

Right. Thanks. Sorry. linas 20:27, 25 November 2006 (UTC)

[edit] Examples

The article needs an example of a topology that satisfies conditions form being an inital toplogy, but is not a final topology. linas 20:14, 20 November 2005 (UTC)