Meritnation Expert,

what is difference between (i) open and simple figures (ii) closed and not simple curves . I can't understand by the videos and notes.

Just have a look at the figure 



Simple curve is a curve which does not cross itself ,need not  be closed 

Open and simple curve is the curve which is simple(i.e does not cross itself) and also not closed .For example Figure 1
Closed and not simple curve is a curve which is closed and also cross itself. For example Figure 4


 

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