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Transactions of the American Mathematical Society

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Examples of $B(D,\lambda )$-refinable and weak $\overline \theta$-refinable spaces


Authors: Stephen H. Fast and J. C. Smith
Journal: Trans. Amer. Math. Soc. 347 (1995), 1803-1809
MSC: Primary 54D20; Secondary 54G20
DOI: https://doi.org/10.1090/S0002-9947-1995-1260165-1
MathSciNet review: 1260165
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Abstract: In 1980, J. C. Smith asked for examples which would demonstrate the relationships between the properties $B(D,\lambda )$-refinability, $B(D,{\omega _0})$-refinability, and weak $\bar \theta$-refinability. This paper gives such examples in the class of ${T_4}$ spaces.


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Keywords: <!– MATH $B(D,\lambda )$ –> <IMG WIDTH="75" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img7.gif" ALT="$B(D,\lambda )$">-refinable, weak <!– MATH $\bar \theta$ –> <IMG WIDTH="16" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$\bar \theta$">-refinable, metacompact, mesocompact, <IMG WIDTH="16" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\theta$">-refinable, compact, Bing space, collectionwise <IMG WIDTH="26" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="${T_2}$">, normal, standard subbasic funnel
Article copyright: © Copyright 1995 American Mathematical Society