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An infinitary version of Sperner's Lemma

Aarno Hohti (2006)

Commentationes Mathematicae Universitatis Carolinae

We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.

An Ulam stability result on quasi-b-metric-like spaces

Hamed H. Alsulami, Selma Gülyaz, Erdal Karapınar, İnci M. Erhan (2016)

Open Mathematics

In this paper a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.

Anosov theorem for coincidences on nilmanifolds

Seung Won Kim, Jong Bum Lee (2005)

Fundamenta Mathematicae

Suppose that L, L’ are simply connected nilpotent Lie groups such that the groups γ i ( L ) and γ i ( L ' ) in their lower central series have the same dimension. We show that the Nielsen and Lefschetz coincidence numbers of maps f,g: Γ∖L → Γ’∖L’ between nilmanifolds Γ∖L and Γ’∖L’ can be computed algebraically as follows: L(f,g) = det(G⁎ - F⁎), N(f,g) = |L(f,g)|, where F⁎, G⁎ are the matrices, with respect to any preferred bases on the uniform lattices Γ and Γ’, of the homomorphisms between the Lie algebras , ’ of...

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