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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spaces with noncoinciding dimensions


Author: M. G. Charalambous
Journal: Proc. Amer. Math. Soc. 94 (1985), 507-515
MSC: Primary 54F45; Secondary 54G20
MathSciNet review: 787903
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Abstract: For any given nonnegative integers $ l,m,n$ with $ \max \{l,m\} \leqslant n$ and $ n = 0$ if $ m = 0$, we construct a normal, Hausdorff and separable space $ X$ with $ \operatorname{ind} X = l,\dim X = m$ and $ \operatorname{ind} X = n$. We also construct a space $ {X_n}$ with $ \dim {X_n} = 1$ and $ \operatorname{ind} {X_n} = \operatorname{Ind}{X_n} = n$ which is the limit space of an inverse limit sequence of compact, Hausdorff and separable spaces all of whose dimensions are one.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0787903-5
PII: S 0002-9939(1985)0787903-5
Keywords: Covering and inductive dimensions, compact, Hausdorff, separable, normal and perfectly normal spaces
Article copyright: © Copyright 1985 American Mathematical Society