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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, <I>p</I>-spaces, <!– MATH ${G_\delta }$ –> <IMG WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img3.gif" ALT="${G_\delta }$">-diagonal, linearly ordered spaces, metrization theorems, <IMG WIDTH="36" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" SRC="images/img6.gif" ALT="$\beta N$">
Article copyright: © Copyright 1973 American Mathematical Society