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Maps with Locally Flat Singular Sets

  • J. G. Timourian (a1)

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A map f : MN is topologically equivalent tog: XY if there exist homeomorphisms α: MX and β: NY such that βfα –1 = g. At xM, f is locally topologically equivalent to g if, for every neighbourhood WM of x, there exist neighbourhoods UW of x and V of f(x) such that f|U: UV is topologically equivalent to g.

1.1. Definition. Given a map f: MN and xM, let F be the component of f –1(f(x)) containing x. The singular set Af is defined as follows: xMAf if and only if there are neighbourhoods U of F and V of f(x) such that f| U: UF is topologically equivalent to the product projection map of V × F onto V.

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References

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Maps with Locally Flat Singular Sets

  • J. G. Timourian (a1)

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