EMBEDDINGS OF NON-METRIC PRODUCTS IN IMAGES OF ORDERED COMPACTA

An important result of L. B. Treybig is that the product of two infinite Hausdorff compact spaces is the continuous image of a compact ordered space if and only if each of the factors is metrizable. Thereafter, A. J. Ward constructed a space that is the continuous image of an ordered compactum and contains the product of a non-metrizable compactum and a (non-compact) infinite discrete space. Herein, we generalize Ward's construction to note that it is relatively straightforward to build continuous images of ordered compacta that nevertheless contain a non-metrizable product. Such spaces have a relatively restricted structure. As a result, one may express in somewhat explicit form a mapping of an ordered compactum onto an appropriate subspace of a compactum containing such a non-metric product.