ArticleOriginal scientific text

Title

The dimension of Xn where X is a separable metric space

Authors 1

Affiliations

  1. George Mason University, Fairfax, Virginia, U.S.A.

Abstract

For a separable metric space X, we consider possibilities for the sequence S(X)={dn:n} where dn=dimXn. In Section 1, a general method for producing examples is given which can be used to realize many of the possible sequences. For example, there is Xn such that S(Xn)={n,n+1,n+2,...}, Yn, for n >1, such that S(Yn)={n,n+1,n+2,n+2,n+2,...}, and Z such that S(Z) = {4, 4, 6, 6, 7, 8, 9,...}. In Section 2, a subset X of 2 is shown to exist which satisfies 1=dimX=dimX2 and dimX3=2.

Bibliography

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm150/fm15015.pdf

Pages:
43-54
Main language of publication
English
Received
1995-09-04
Accepted
1995-11-17
Published
1996
Exact and natural sciences