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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An example concerning inverse limit sequences of normal spaces


Author: M. G. Charalambous
Journal: Proc. Amer. Math. Soc. 78 (1980), 605-607
MSC: Primary 54F45; Secondary 54B25, 54D15, 54D20
DOI: https://doi.org/10.1090/S0002-9939-1980-0556641-1
MathSciNet review: 556641
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Abstract: Using techniques developed by Wage and Przymusiński, we construct an inverse limit sequence $({X_n},{f_{nm}})$ with limit space X such that each ${X_n}$ is Lindolöf with $\dim {X_n} = 0$, where dim denotes covering dimension, while X is normal with $\dim X > 0$. The space X is a counterexample to several conjectures in Topology.


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Keywords: Normal, Lindel&#246;f, paracompact, topologically complete and <I>N</I>-compact space, covering dimension
Article copyright: © Copyright 1980 American Mathematical Society