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Are there continuous bijections whose inverse is not continuous?
I see. Is this a common occurrence in topology?
It depends on the context. In certain branches of topology, such as algebraic topology, the focus is on continuous functions that preserve certain algebraic structures, and in these cases, it is often the case that continuous bijections have continuous inverses. However, in general topology and geometric topology, there are many examples of continuous bijections that do not have continuous inverses.