On weakly infinite-dimensional subspuees

P. Borst

Fundamenta Mathematicae (1992)

  • Volume: 140, Issue: 3, page 225-235
  • ISSN: 0016-2736

Abstract

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We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and d i m Y = ω 0 and d i m X = ω 0 + 1 . Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.

How to cite

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Borst, P.. "On weakly infinite-dimensional subspuees." Fundamenta Mathematicae 140.3 (1992): 225-235. <http://eudml.org/doc/211942>.

@article{Borst1992,
abstract = {We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and $dim Y = ω_0$ and $dim X = ω_0 + 1$. Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.},
author = {Borst, P.},
journal = {Fundamenta Mathematicae},
keywords = {weakly infinite-dimensional; transfinite dimension; weakly infinite-dimensional space},
language = {eng},
number = {3},
pages = {225-235},
title = {On weakly infinite-dimensional subspuees},
url = {http://eudml.org/doc/211942},
volume = {140},
year = {1992},
}

TY - JOUR
AU - Borst, P.
TI - On weakly infinite-dimensional subspuees
JO - Fundamenta Mathematicae
PY - 1992
VL - 140
IS - 3
SP - 225
EP - 235
AB - We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and $dim Y = ω_0$ and $dim X = ω_0 + 1$. Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.
LA - eng
KW - weakly infinite-dimensional; transfinite dimension; weakly infinite-dimensional space
UR - http://eudml.org/doc/211942
ER -

References

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  1. [B1] P. Borst, Classification of weakly infinite-dimensional spaces. Part I: A transfinite extension of the covering dimension, Fund. Math. 130 (1988), 1-25. Zbl0661.54035
  2. [B2] P. Borst, Classification of weakly infinite-dimensional spaces. Part II: Essential mappings, ibid., 73-99. Zbl0661.54036
  3. [Ch] V. A. Chatyrko, On the transfinite dimension dim, to appear. Zbl0774.54024
  4. [E1] R. Engelking, General Topology, PWN, Warszawa 1977. 
  5. [E2] R. Engelking, Dimension Theory, PWN, Warszawa 1978. 
  6. [He] D. W. Henderson, A lower bound for transfinite dimension, Fund. Math. 63 (1968), 167-173. Zbl0167.51301
  7. [L] L. A. Lyuksemburg, On transfinite inductive dimensions, Soviet Math. Dokl. 14 (1973), 388-393. Zbl0283.54019
  8. [P] R. Pol, On classification of weakly infinite-dimensional compacta, Fund. Math. 116 (1983), 169-188. Zbl0571.54030

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