Is Bifurcation Topologically the Same?

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rsaad
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Hi I have not taken nay course in Topology. So can someone please explain what it means to say "in the neighborhood of some point bifurcation is topologically same"?
thank you.
 
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As you have written it, it doesn't mean anything. What is "topologically the same" as what?
 
If you compare both sides of the bifurcation point, they are topologically same.
 

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