# On weakly infinite-dimensional subspuees

Fundamenta Mathematicae (1992)

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

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topBorst, 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

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

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