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Coincidence theorems and minimax inequalities in abstract convex spaces
In this paper, we deal with the notion of abstract convex spaces via minimal spaces as an extended version of other forms of convexity and establish...
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The topological Tverberg theorem and related topics
The classical Borsuk–Ulam theorem, established some eighty years ago, may now be seen as a consequence of the nonvanishing of the mod 2 cohomology...
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Some new fixed point theorems for set-valued contractions in complete metric spaces
In this article, we obtain some new fixed point theorems for set-valued contractions in complete metric spaces. Our results generalize or improve...
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Applications of some basic theorems in the KKM theory
In this review, we introduce a new KKM-type theorem for intersectionally closed-valued KKM map on abstract convex spaces and its direct consequences...
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A simple proof of Olatinwo’s theorems
In this paper we provide a simple proof of the existence coupled fixed point theorem in complete cone metric spaces due to Sabetghadam et al. (Fixed...
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On approximation of asymmetric separators of the n-cube
A new combinatorial result intertwined with the Brouwer fixed point theorem for the n -cube is given. This result can be used for any map ( f 1 , ..., fn )...
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Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
Let M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological...
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Fixed-orbit indices, I
Let G be a compact Lie group. Using methods from equivariant fibrewise stable homotopy theory, we study indices which measure algebraically (1) for a G ...
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The Borsuk–Ulam theorem for homotopy spherical space forms
In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk–Ulam theorem holds. These spaces are the quotient of a...
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A Reidemeister trace for fibred maps
A Reidemeister trace for fibred maps is defined as the alternating sum of suitable (elementary) traces for linear morphisms of fibred cellular free...
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A Hopf type classification theorem for isovariant maps from free G-manifolds to representation spheres
An isovariant map is an equivariant map preserving the isotropy subgroups. In this paper, we develop an isovariant version of the Hopf classification...
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Minimum numbers and Wecken theorems in topological coincidence theory. I
Minimum numbers measure the obstruction to removing coincidences of two given maps (between smooth manifolds M and N of dimensions m and n , resp.)....
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The finiteness of the Reidemeister number of morphisms between almost-crystallographic groups
We give a practical criterion to determine whether a given pair of morphisms between almost-crystallographic groups has a finite Reidemeister...
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Strong surjectivity of maps from 2-complexes into the 2-sphere
Given a model 2-complex K P of a group presentation P , we associate to it an integer matrix Δ P and we prove that a cellular map f : K ...
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Orbit Spaces of Free Involutions on the Product of Two Projective Spaces
Let X be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on X and determine...