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2012-03-27 Nonlinear Seminar

Piotr Maćkowiak
Exploding points

We will present and prove theorem of the exploding point. This theorem states that for any function defined on a compact set X, containing the cube K centered at zero in its interior, with values ​​in X\K, which is the identity on the boundary of the set X, there exists a point c in X, that in any surroundings of c, there is a point x such that the value of f(x) and f(c) are located on opposite walls of the cube K.