K.L. Kozlov

On an approach to constructing compacta with different dimensions dim and ind

Abstract In this paper we reveal common features in the constructions of some compacta X with dim X ind X . To any regular T 1 -space X a class T(X) of regular T 1 -spaces is related. Elements of T(X) are called tailings of X . Two concrete types of tailings are described. For any compactum X with dim X= ind X>0 , these constructions allow to obtain compacta Y with dim Y= dim X and ind Y> dim X . At the end of the paper, using tailings, we present compacta with different dimensions dim and ind constructed by means of product formation starting from compacta with equal dim and ind .