Talk:Initial topology

Coarsest topology

I removed the following from the examples section:

Given a family of topologies {τ_i} on a fixed set X the initial topology on X with respect to the functions id_X : X → (X, τ_i) is the supremum (or join) of the topologies {τ_i} in the lattice of topologies on X. That is, the initial topology τ is the topology generated by the union of the topologies {τ_i}.

See Talk:Final topology for a discussion why. (Basically, the join of topologies will be finer or stronger than any of he individual τ_i, which contradicts the idea that the inital topology is the coarsest topology). linas 20:51, 20 November 2005 (UTC)[reply]

Dohh, my mistake, never mind, restored. linas 02:41, 6 March 2007 (UTC)[reply]

Blank and redirect from Induced topology

By its own admission, Induced topology covered exactly the same topics as Final topology and Initial topology. All encyclopedic content that was there was already contained in the remaining two articles. Therefore I blanked Induced topology and redirected to Initial topology (Coinduced topology was already a redirect to Final topology). Felix QW (talk) 20:36, 8 January 2022 (UTC)[reply]