A factorization theorem for the transfinite kernel dimension of metrizable spaces

M. Charalambous

Fundamenta Mathematicae (1998)

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

Abstract

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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.

How to cite

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Charalambous, 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

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

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