A Note on Complete Collectionwise Normality and Paracompactness

1. A question that has aroused considerable interest and which has remained unanswered is the following. Is a normal Moore space metrizable? Both R. H. Bing and F. B. Jones have important results which go a long way toward answering this question. For example, Bing has proved that a collectionwise normal Moore space is metrizable [l ] while Jones has shown that a separable normal Moore space is metrizable [2] provided the continuum hypothesis holds true. Although the results given in the present paper fail to answer the question at hand, it is shown that certain types of normality and paracompactness are equivalent in a Moore space, indeed, in more abstract spaces such as a semimetric topological space.2