Pairwise monotonically normal spaces.
Marín, Josefa, Romaguera, Salvador (1991)
Commentationes Mathematicae Universitatis Carolinae
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Marín, Josefa, Romaguera, Salvador (1991)
Commentationes Mathematicae Universitatis Carolinae
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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. ...
Maksa, Gyula, Nizsalóczki, Enikő (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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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
Ballico, E., Cossidente, A. (1996)
Mathematica Pannonica
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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...
Agarwal, Ravi P., O'Regan, Donal (2001)
Georgian Mathematical Journal
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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 . We also construct a solution of the equation in that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.