On the number of fixed points for a continuous map of a finite connected graph.
On the Schauder fixed point theorem
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.
On the sharpness of the ... 2 and ... 1 Nielsen numbers.
On the singularity of Mazurkiewicz in absolute neighborhood retracts
On the structure of the set of solutions of a functional equation with applications to boundary value problems
On the théorème fondamental of J. Leray and J. Schauder
On the uniqueness of the fixed point index on differentiable manifolds.
On the Uniqueness of the Topological Degree.
On the Uniqueness of the Topological Degree for k-Set-Contractions.
On the winding number and equivariant homotopy classes of maps of manifolds with some finite group actions
On two results of Singhof
For a compact connected semisimple Lie group we shall prove two results (both related with Singhof’s paper [13]) on the Lusternik-Schnirelmann category of the adjoint orbits of , respectively the 1-dimensional relative category of a maximal torus in . The techniques will be classical, but we shall also apply some basic results concerning the so-called -category (cf. [14]).
On universality of countable and weak products of sigma hereditarily disconnected spaces
Suppose a metrizable separable space Y is sigma hereditarily disconnected, i.e., it is a countable union of hereditarily disconnected subspaces. We prove that the countable power of any subspace X ⊂ Y is not universal for the class ₂ of absolute -sets; moreover, if Y is an absolute -set, then contains no closed topological copy of the Nagata space = W(I,ℙ); if Y is an absolute -set, then contains no closed copy of the Smirnov space σ = W(I,0). On the other hand, the countable power of...
On Whitehead's inequality, .
On Δ-spaces and fundamental dimension in the sense of Borsuk
Once More on the Lefschetz Fixed Point Theorem
An abstract version of the Lefschetz fixed point theorem is presented. Then several generalizations of the classical Lefschetz fixed point theorem are obtained.
One codimensional Wecken type theorems.
One-parameter Fixed Point Theory.
Optimal bounds for the colored Tverberg problem
We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.
Parametrized Borsuk-Ulam problem for projective space bundles
Let π: E → B be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let π’: E’ → B be a vector bundle such that ℤ₂ acts fiber preserving and freely on E and E’-0, where 0 stands for the zero section of the bundle π’: E’ → B. For a fiber preserving ℤ₂-equivariant map f: E → E’, we estimate the cohomological dimension of the zero set . As an application, we also estimate the cohomological dimension of the ℤ₂-coincidence set of a fiber preserving...
Parametrized Borsuk-Ulam theorems.