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Proceedings of the American Mathematical Society

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

 

 

On the realization of the metric-dependent dimension function $ d\sb{2}$


Author: Tatsuo Goto
Journal: Proc. Amer. Math. Soc. 58 (1976), 265-271
MSC: Primary 54F45
DOI: https://doi.org/10.1090/S0002-9939-1976-0410698-6
MathSciNet review: 0410698
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Abstract: Let $ (X,\rho )$ be a metric space with $ {d_2}(X,\rho ) < \dim X$ where $ {d_2}$ denotes the metric-dependent dimension function introduced by K. Nagami and J. H. Roberts [2]. Then it will be shown that for any integer $ k$ with $ {d_2}(X,\rho ) \leq k \leq \dim X$ there exists a topologically equivalent metric $ {\rho _k}$ with $ {d_2}(X,{\rho _k}) = k$. This extends a result of J. C. Nichols [3] and answers the problem raised by K. Nagami and J. H. Roberts [2] in the affirmative.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0410698-6
Keywords: Metric spaces, metric-dependent dimension $ {d_2}$, realizations of $ {d_2}$
Article copyright: © Copyright 1976 American Mathematical Society