### Monotone Explicit Iterations of the Finite Element Approximations for the Nonlinear Boundary Value Problem.

Kazuo Ishihara (1984)

Numerische Mathematik

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Kazuo Ishihara (1984)

Numerische Mathematik

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Kvinikadze, G. (1999)

Memoirs on Differential Equations and Mathematical Physics

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Lj. Kočinac (1991)

Matematički Vesnik

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Marko Švec (1967)

Colloquium Mathematicae

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Ian Stares (1995)

Commentationes Mathematicae Universitatis Carolinae

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We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of ${K}_{0}$-spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions.

Philip Hartman (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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N.L. Schryer (1971/72)

Numerische Mathematik

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Nikolaos S. Papageorgiou (1991)

Publications de l'Institut Mathématique

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Volle, M. (1994)

Journal of Convex Analysis

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Aleš Nekvinda, Ondřej Zindulka (2011)

Fundamenta Mathematicae

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A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.