On A Universal Bicompactum of Weight N

Abstract

According to the well-known theorem by P. Alexandrov, the Cantor discontinuum \({\Delta_{{N_0}}}\) has the universality property in the class of all compact spaces of weight ≤ N0- The universality property means that every compact space of weight ≤ N0 is its continuous image. P. Alexandrov also gave a simple topological definition of ∆n0 as a zero-dimensional perfect compact space of weight N0. In [1], A. Esenin-Vol’pin, assuming the generalized continuum hypothesis, proved the existence of a compact space of an arbitrary weight m, which is universal in the same sense.