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Equivariant maps of joins of finite G-sets and an application to critical point theory

Danuta Rozpłoch-Nowakowska — 1992

Annales Polonici Mathematici

A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function $f : S^{n} \to ℝ$ , where G is a finite nontrivial group acting freely and orthogonally on $ℝ^{n + 1} 0$ . Neither Morse theory nor the minimax method is applied. The proofs are based on a general version of Borsuk’s Antipodal Theorem for equivariant maps of joins of G-sets.

On the Schauder fixed point theorem

Lech Górniewicz; Danuta Rozpłoch-Nowakowska — 1996

Banach Center Publications

The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.

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