A note on transfinite inductive dimension of a space by a normal base
by
Dimitris Georgiou
University of Patras, Departmeny of Mathematics, 265 04 Patras, Greece.
Coauthors: S.D. Iliadis and K.L. Kozlov

Abstract. In [2] dimension-like functions of type Ind on a space by a normal base (see [5]) are given. These functions generalize dimensions Ind and Ind₀ (see [4]), as well as, relative dimensions of [3]. In [2] they are studied only with respect to the existence of universal elements. In [1] other standard properties of dimension theory for the finite variant of these functions are studied. Here, we study the transfinite variant of these functions.

References

[1] D.N. Georgiou, S.D. Iliadis and K.L. Kozlov, Base normal inductive dimension (submitted for publication).

[2] S. D. Iliadis, Universal spaces and mappings. North-Holland Mathematics Studies, 198. Elsevier Science B.V., Amsterdam, 2005. xvi+559 pp.

[3] A. Chigogidze, On relative dimensions, General Topology. Spaces of functions and dimension, Moscow State University, Moscow, 1985, 67—117.

[4] A. V. Ivanov, On the dimension of non perfectly normal spaces, Bull. Moscow State University, 1976, N 4, 21-27.

[5] O. Frink, Compactifications and semi-normal spaces, Amer. J. Math., 1964, v. 86, N 3, 602-607.

Date received: April 11, 2008