A factorization theorem for the transfinite kernel dimension of metrizable spaces

• Autorzy: M. G. Charalambous
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 157
• Numer: 1
• Strony: 79-84

Daty

wydano

1998

otrzymano

1997-08-14

poprawiono

1997-12-15

Twórcy

autor

M. G. Charalambous

• Department of Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece

Bibliografia

• [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.
• [4] L. Luxemburg, On universal infinite-dimensional spaces, Fund. Math. 122 (1984), 129-144.
• [5] W. Olszewski, On D-dimension of metrizable spaces, ibid. 140 (1991), 35-48.
• [6] B. A. Pasynkov, On universal bicompacta of a given weight and dimension, Soviet Math. Dokl. 5 (1964), 245-246.
• [7] B. A. Pasynkov, A factorization theorem for non-closed sets, ibid. 13 (1972), 292-295.