Is Bifurcation Topologically the Same?

[rsaad]

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.

 

[HallsofIvy]

As you have written it, it doesn't mean anything. What is "topologically the same" as what?

 

[rsaad]

If you compare both sides of the bifurcation point, they are topologically same.