Definition
Given a set X and an indexed family (Yi)i∈I of topological spaces with functions
the initial topology τ on is the coarsest topology on X such that each
is continuous.
Explicitly, the initial topology may be described as the topology generated by sets of the form, where is an open set in . The sets are often called cylinder sets. If I contains just one element, all the open sets of are cylinder sets.
Read more about this topic: Initial Topology
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