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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Monotonically normal spaces

Authors: R. W. Heath, D. J. Lutzer and P. L. Zenor
Journal: Trans. Amer. Math. Soc. 178 (1973), 481-493
MSC: Primary 54E20
MathSciNet review: 0372826
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Abstract: This paper begins the study of monotone normality, a common property of linearly ordered spaces and of Borges' stratifiable spaces. The concept of monotone normality is used to give necessary and sufficient conditions for stratifiability of a $ {T_1}$-space, to give a new metrization theorem for p-spaces with $ {G_\delta }$-diagonals, and to provide an easy proof of a metrization theorem due to Treybig. The paper concludes with a list of examples which relate monotone normality to certain familiar topological properties.

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Keywords: Monotone normality, collectionwise normality, stratifiable spaces, extension theorems, p-spaces, $ {G_\delta }$-diagonal, linearly ordered spaces, metrization theorems, $ \beta N$
Article copyright: © Copyright 1973 American Mathematical Society