Relationen für primäre Homotopieoperationen und eine verallgemeinerte EHP-Sequenz
In this paper, we clarify the relationship among the Vietoris-type homology theories and the microsimplicial homology theories, where the latter are nonstandard homology theories defined by M.C. McCord (for topological spaces), T. Korppi (for completely regular topological spaces) and the author (for uniform spaces). We show that McCord’s and our homology are isomorphic for all compact uniform spaces and that Korppi’s and our homology are isomorphic for all fine uniform spaces. Our homology shares...
Let (X,A) be a pair of topological spaces, T : X → X a free involution and A a T-invariant subset of X. In this context, a question that naturally arises is whether or not all continuous maps have a T-coincidence point, that is, a point x ∈ X with f(x) = f(T(x)). In this paper, we obtain results of this nature under cohomological conditions on the spaces A and X.
We describe the structure of minimal round functions on compact closed surfaces and three-dimensional manifolds. The minimal possible number of critical loops is determined and typical non-equisingular round function germs are interpreted in the spirit of isolated line singularities. We also discuss a version of Lusternik-Schnirelmann theory suitable for round functions.