Displaying similar documents to “K-monotone Spaces between Spaces of Absolutely Summable Series.”

Monotone normality and extension of functions

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.

A Cantor set in the plane that is not σ-monotone

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.

Monotone interval eigenproblem in max–min algebra

Martin Gavalec, Ján Plavka (2010)

Kybernetika

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The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented.