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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.