Geodesic
Moore Spaces, Semi-Metric Spaces and Continuous Mappings Connected with Them
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1033-1042

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In [1] Arhangel'skiĭ announced that any σ-paracompact p-space could be mapped onto a Moore space by a perfect map. However Burke [3] recently showed that this is not true in general and he gave an example of a T2 , locally compact, σ-paracompact space which cannot be mapped onto a Moore space by a perfect map. 
Pareek, C. M. Moore Spaces, Semi-Metric Spaces and Continuous Mappings Connected with Them. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1033-1042. doi: 10.4153/CJM-1972-105-8
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[1] 1. Arhangel'skii, A. V., Mappings and spaces, Russian Math. Surveys 21 (1966), 115–162. Google Scholar

[2] 2. Bing, R. H., Metrization of topological spaces, Can. J. Math. 3 (1951), 175–186. Google Scholar

[3] 3. Burke, D. K., Subparacompact spaces, Proc. of the Washington State University conference on general topology (March 1970), 39-49. Google Scholar

[4] 4. Ceder, J. G., Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105–125. Google Scholar

[5] 5. McAuley, L. F., A note on complete collectionwise normality and paracompactness, Proc. Amer. Math. Soc. 9 (1958), 796–799. Google Scholar

[6] 6. Pareek, C. M., Characterization of p-spaces, Can. Math. Bull. 14 (1971), 459–460. Google Scholar

[7] 7. Ponomarev, V. I., On paracompact and finally compact spaces, Soviet Math. Dokl. 2 (1961), 1510–1512. Google Scholar

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