Edivaldo L. dos Santos

The implicit function theorem for continuous functions

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of these classic theorems are proved when we consider differenciable (not necessarily C^1) maps.

Bourgin–Yang versions of the Borsuk–Ulam theorem for p-toral groups

Let V and W be orthogonal representations of G with

(H,G)

V^G= W^G=\{0\}

On path-components of the mapping spaces \(M(\mathbb {S}^m,\mathbb {F}P^n)\)

VG=WG={0}. Let S(V ) be the sphere of V and

Borsuk-Ulam theorems and their parametrized versions for spaces of type .a;b/

f : S(V ) \rightarrow W

Bourgin–Yang version of the Borsuk–Ulam theorem for ℤpk–equivariant maps

f:S(V)→W be a G-equivariant mapping. We give an estimate for the dimension of the set