Geodesic
On the Existence of Normal Metacompact Moore Spaces which are not Metrizable
Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 1-6

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It is known that the following classes of spaces (all spaces in this article are assumed T1) are identical:1. Images of metric spaces under continuous open maps with compact point inverses.2. Spaces with uniform bases (in the sense of Alexandrov [1]).3. Metacompact developable spaces.4. Spaces with σ-point-finite bases in which closed sets are G δ's. 
Tall, Franklin D. On the Existence of Normal Metacompact Moore Spaces which are not Metrizable. Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 1-6. doi: 10.4153/CJM-1974-001-8
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[1] 1. Aleksandrov, P. S., On the metrization of topological spaces, (in Russian), Bull. Acad. Polon. Sri. Sér. Sci. Math. Astronom. Phys. 8 (1960), 135–140. Google Scholar

[2] 2. Arhangel'skii, A. V., On mappings of metric spaces, Soviet Math. Dokl. 3 (1962), 953–956. Google Scholar

[3] 3. Arhangel'skii, A. V., Mappings and spaces, Russian Math. Surveys 21 (1966), 87–114. Google Scholar

[4] 4. Arhangel'skii, A. V., The property of paracompactness in the class of perfectly normal, locally bicompact spaces, Soviet Math. Dokl. 13 (1972), 517–520. Google Scholar

[5] 5. Aull, C. E., Topological spaces with a σ-point-finite base, Proc. Amer. Math. Soc. 29 (1971), 411–416. Google Scholar

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

[7] 7. Bing, R. H., A translation of the normal Moore space conjecture, Proc. Amer. Math. Soc. 16 (1965), 612–619. Google Scholar

[8] 8. Borges, C. J. R., On metrizability of topological spaces, Can. J. Math. 20 (1968), 795–804. Google Scholar

[9] 9. Coban, M. M., On o∼-paracompact spaces, (in Russian), Vestnik Moskov. Univ. Ser. I Mat. Meh. (1969), 20-27. Google Scholar

[10] 10. Corson, H. H. and Michael, E., Metrizability of certain countable unions, Illinois J. Math. 8 (1964), 351–360. Google Scholar

[11] 11. Creede, G. D., Embedding of complete Moore spaces, Proc. Amer. Math. Soc. 28 (1971), 609–612. Google Scholar

[12] 12. Fitzpatrick, B., On dense subspaces of Moore spaces, II, Fund. Math. 61 (1967), 91–92. Google Scholar

[13] 13. Hanai, S., On open mappings, II, Proc. Japan Acad. 37 (1961), 233–238. Google Scholar

[14] 14. Heath, R. W., Screenability, pointwise paracompactness and metrization of Moore spaces, Can. J. Math. 16 (1964), 763–770. Google Scholar

[15] 15. Martin, D. and Solovay, R. M., Internal Cohen extensions, Ann. Math. Logic 2 (1970), 143–178. Google Scholar

[16] 16. Przymusinski, T. and Tall, F. D., The undecidability of the existence of a non-separable normal Moore space satisfying the countable chain condition, Fund. Math, (to appear). Google Scholar

[17] 17. Reed, G. M., On dense subspaces, pp. 337-344 in Proc. Univ. Okla. Top. Conf. 1972, Norman, Oklahoma, 1972. Google Scholar

[18] 18. Shiraki, T., A note on spaces with a uniform base, Proc. Japan Acad. 47 (1971), 1036–1041. Google Scholar

[19] 19. Solovay, R. M. and S. Tennenbaum, Iterated Cohen extensions and Souslin's problem, Ann. of Math. 94 (1971), 201–245. Google Scholar

[20] 20. Steen, L. A. and Seebach, J. A., Counterexamples in topology (Holt Rinehart and Winston, New York, 1970). Google Scholar

[21] 21. Tall, F. D., Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems, Ph.D. thesis, University of Wisconsin, 1969. Google Scholar

[22] 22. Tall, F. D., A counterexample in the theories of compactness and of metrization, Proc. Kon. Ned. Akad. van Wetensch., Amsterdam, Series A (to appear). Google Scholar

[23] 23. Tall, F. D., An alternative to the continuum hypothesis and its uses in general topology (preprint). Google Scholar

[24] 24. Traylor, D. R., Concerning metrizability of pointwise paracompact Moore spaces, Can. J. Math. 16 (1966), 407–411. Google Scholar

[25] 25. Traylor, D. R., Metrizability and completeness in normal Moore spaces, Pacific J. Math. 17 (1966), 381–390. Google Scholar

[26] 26. Traylor, D. R., Metrizability in normal Moore spaces, Pacific J. Math. 19 (1966), 174–181. Google Scholar

[27] 27. Traylor, D. R., On normality, pointwise paracompactness and the metrization question, pp. 286-289 in Topology Conference Arizona State University, 1967, Tempe, Arizona, 1968. Google Scholar

[28] 28. Worrell, J. M., Jr., On continuous mappings of metacompact Čech complete spaces, Pacific J. Math. 30 (1969), 555–562. Google Scholar

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