Displaying similar documents to “An application of the topological rigidity of the sine family.”

Pairwise monotonically normal spaces

Josefa Marín, Salvador Romaguera (1991)

Commentationes Mathematicae Universitatis Carolinae

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We introduce and study the notion of pairwise monotonically normal space as a bitopological extension of the monotonically normal spaces of Heath, Lutzer and Zenor. In particular, we characterize those spaces by using a mixed condition of insertion and extension of real-valued functions. This result generalizes, at the same time improves, a well-known theorem of Heath, Lutzer and Zenor. We also obtain some solutions to the quasi-metrization problem in terms of the pairwise monotone normality. ...

Quasi-sums in several variables.

Maksa, Gyula, Nizsalóczki, Enikő (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Heron's Formula and Ptolemy's Theorem

Marco Riccardi (2008)

Formalized Mathematics

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The goal of this article is to formalize some theorems that are in the [17] on the web. These are elementary theorems included in every handbook of Euclidean geometry and trigonometry: the law of cosines, the Heron's formula, the isosceles triangle theorem, the intersecting chords theorem and the Ptolemy's theorem.MML identifier: EUCLID 6, version: 7.8.09 4.97.1001

Tietze Extension Theorem for n-dimensional Spaces

Karol Pąk (2014)

Formalized Mathematics

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In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic...

On nodal sets and nodal domains on S 2 and ℝ 2

Alexandre Eremenko, Dmitry Jakobson, Nikolai Nadirashvili (2007)

Annales de l’institut Fourier

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We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S 2 . We also construct a solution of the equation Δ u = u in ℝ 2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.