When we study topology, we typically study topological spaces and continuous maps between them. From a categorical perspective, this is "wrong," because continuous maps are not the structure preserving maps. If "the structure of a topological space" is it's topology (i.e., it's open sets) then it seems like the natural choice for the definition of a structure preserving map would be an open map. So why do we like continuous maps instead of open maps?
2026-04-06 01:37:52.1775439472
Continuous maps vs. open maps
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