ON THE CAPACITY OF EILENBERG-MACLANE AND MOORE SPACES

Abstract

K. Borsuk in 1979, at the Topological Conference in Moscow, introduced concept of the capacity of a compactum and asked some questions concerning properties of the capacity of<br />compacta. In this paper, we give partial positive answers to three of these questions in some cases. In fact, by describing spaces homotopy dominated by Moore and Eilenberg-MacLane spaces, the capacities of a Moore space $M(A,n)$ and an Eilenberg-MacLane space $K(G,n)$ could be obtained. Also, we compute the capacity of wedge sum of finitely many Moore spaces of different degrees and the capacity of product of finitely many Eilenberg-MacLane spaces of different homotopy types. In particular, we compute the capacity of wedge sum of finitely many spheres of the same or different dimensions.<br /><br />