Talk:Initial topology
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[edit] Coarsest topology
I removed the following from the examples section:
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- Given a family of topologies {τi} on a fixed set X the initial topology on X with respect to the functions idX : X → (X, τi) is the supremum (or join) of the topologies {τi} in the lattice of topologies on X. That is, the initial topology τ is the topology generated by the union of the topologies {τi}.
See Talk:Final topology for a discussion why. (Basically, the join of topologies will be finer or stronger than any of he individual τi, which contradicts the idea that the inital topology is the coarsest topology). linas 20:51, 20 November 2005 (UTC)
