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Relationship among various Vietoris-type and microsimplicial homology theories

Takuma Imamura (2021)

Archivum Mathematicum

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...

Relative Borsuk-Ulam Theorems for Spaces with a Free ℤ₂-action

Denise de Mattos, Thaís F. M. Monis, Edivaldo L. dos Santos (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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 f : X → ℝ k 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.

Remarks on minimal round functions

Georgi Khimshiashvili, Dirk Siersma (2003)

Banach Center Publications

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.

Currently displaying 61 – 80 of 108