# A factorization theorem for the transfinite kernel dimension of metrizable spaces

Fundamenta Mathematicae (1998)

- Volume: 157, Issue: 1, page 79-84
- ISSN: 0016-2736

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topCharalambous, M.. "A factorization theorem for the transfinite kernel dimension of metrizable spaces." Fundamenta Mathematicae 157.1 (1998): 79-84. <http://eudml.org/doc/212279>.

@article{Charalambous1998,

abstract = {We prove a factorization theorem for transfinite kernel dimension in the class of metrizable spaces. Our result in conjunction with Pasynkov's technique implies the existence of a universal element in the class of metrizable spaces of given weight and transfinite kernel dimension, a result known from the work of Luxemburg and Olszewski.},

author = {Charalambous, M.},

journal = {Fundamenta Mathematicae},

keywords = {covering dimension; transfinite kernel dimension; -dimension},

language = {eng},

number = {1},

pages = {79-84},

title = {A factorization theorem for the transfinite kernel dimension of metrizable spaces},

url = {http://eudml.org/doc/212279},

volume = {157},

year = {1998},

}

TY - JOUR

AU - Charalambous, M.

TI - A factorization theorem for the transfinite kernel dimension of metrizable spaces

JO - Fundamenta Mathematicae

PY - 1998

VL - 157

IS - 1

SP - 79

EP - 84

AB - We prove a factorization theorem for transfinite kernel dimension in the class of metrizable spaces. Our result in conjunction with Pasynkov's technique implies the existence of a universal element in the class of metrizable spaces of given weight and transfinite kernel dimension, a result known from the work of Luxemburg and Olszewski.

LA - eng

KW - covering dimension; transfinite kernel dimension; -dimension

UR - http://eudml.org/doc/212279

ER -

## References

top- [1] M. G. Charalambous, Further theory and applications of covering dimension of uniform spaces, Czechoslovak Math. J. 41 (1991), 378-394.
- [2] R. Engelking, Theory of Dimensions, Finite and Infinite, Sigma Ser. Pure Math. 10, Heldermann, Lemgo, 1995.
- [3] D. W. Henderson, D-dimension, I. A new transfinite dimension, Pacific J. Math. 26 (1968), 91-107. Zbl0162.26904
- [4] L. Luxemburg, On universal infinite-dimensional spaces, Fund. Math. 122 (1984), 129-144. Zbl0571.54029
- [5] W. Olszewski, On D-dimension of metrizable spaces, ibid. 140 (1991), 35-48. Zbl0807.54007
- [6] B. A. Pasynkov, On universal bicompacta of a given weight and dimension, Soviet Math. Dokl. 5 (1964), 245-246. Zbl0197.48601
- [7] B. A. Pasynkov, A factorization theorem for non-closed sets, ibid. 13 (1972), 292-295. Zbl0247.54037

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