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In common textbooks' discussions about conservative vector field. There is always two assumptions about the region concerned, namely the region is simply connected and open.

Usually in textbooks there is not much explanations on why these assumptions are necessary, no proof is given on why conservative field is not possible if the region is not simply connected or not open.

I wonder whether these two assumptions are just for computational convenience or it is really logically not possible to have a conservative field in region that is not simply connected or is not open?

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# Question about conditions for conservative field

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