5 papers
Higher order Nielsen numbers
Peter Saveliev
Suppose X,Y are manifolds, f,g:X->Y are maps. The well-known Coincidence Problem studies the coincidence set C={x:f(x)=g(x)}. The number m=dimX-dimY is called the codimension of th…
Removing coincidences of maps between manifolds of different dimensions
Peter Saveliev
We consider sufficient conditions of local removability of coincidences of maps f,g:N->M, where M,N are manifolds with dimensions dimN>dimM. The coincidence index is the only obstr…
Lomonosov's Invariant Subspace Theorem for Multivalued Linear Operators
Peter Saveliev
The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator…
Lefschetz Coincidence Theory for Maps Between Spaces of Different Dimensions
Peter Saveliev
For a given pair of maps f,g:X->M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism L:H(X)->H(M) of degree (-n). We…
Fixed points and selections of multifunctions on spaces with convexity
Peter Saveliev
We provide theorems containnig both Kakutani and Browder fixed points theorems as immediate corollaries, as well as Michael and Browder selection theorems. For this purpose we intr…