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Created page with "It would be more precise to describe a topological space as a set along with some subset of its power set, designated the open sets. The open sets do not generate the topology, ..."
It would be more precise to describe a topological space as a set along with some subset of its power set, designated the open sets. The open sets do not generate the topology, they ARE the topology. A basis for a topology generates the topology. Also, it might be worthwhile to describe what properties the open sets have to satisfy (e.g. closure under finite intersections and arbitrary unions).