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On the Existence of Normal Metacompact Moore Spaces which are not Metrizable

  • Franklin D. Tall (a1)

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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.

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References

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1. Aleksandrov, P. S., On the metrization of topological spaces, (in Russian), Bull. Acad. Polon. Sri. Sér. Sci. Math. Astronom. Phys. 8 (1960), 135140.
2. Arhangel'skii, A. V., On mappings of metric spaces, Soviet Math. Dokl. 3 (1962), 953956.
3. Arhangel'skii, A. V., Mappings and spaces, Russian Math. Surveys 21 (1966), 87114.
4. Arhangel'skii, A. V., The property of paracompactness in the class of perfectly normal, locally bicompact spaces, Soviet Math. Dokl. 13 (1972), 517520.
5. Aull, C. E., Topological spaces with a σ-point-finite base, Proc. Amer. Math. Soc. 29 (1971), 411416.
6. Bing, R. H., Metrization of topological spaces, Can. J. Math. 3 (1951), 175186.
7. Bing, R. H., A translation of the normal Moore space conjecture, Proc. Amer. Math. Soc. 16 (1965), 612619.
8. Borges, C. J. R., On metrizability of topological spaces, Can. J. Math. 20 (1968), 795804.
9. Coban, M. M., On o∼-paracompact spaces, (in Russian), Vestnik Moskov. Univ. Ser. I Mat. Meh. (1969), 20-27.
10. Corson, H. H. and Michael, E., Metrizability of certain countable unions, Illinois J. Math. 8 (1964), 351360.
11. Creede, G. D., Embedding of complete Moore spaces, Proc. Amer. Math. Soc. 28 (1971), 609612.
12. Fitzpatrick, B., On dense subspaces of Moore spaces, II, Fund. Math. 61 (1967), 9192.
13. Hanai, S., On open mappings, II, Proc. Japan Acad. 37 (1961), 233238.
14. Heath, R. W., Screenability, pointwise paracompactness and metrization of Moore spaces, Can. J. Math. 16 (1964), 763770.
15. Martin, D. and Solovay, R. M., Internal Cohen extensions, Ann. Math. Logic 2 (1970), 143178.
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).
17. Reed, G. M., On dense subspaces, pp. 337-344 in Proc. Univ. Okla. Top. Conf. 1972, Norman, Oklahoma, 1972.
18. Shiraki, T., A note on spaces with a uniform base, Proc. Japan Acad. 47 (1971), 10361041.
19. Solovay, R. M. and S. Tennenbaum, Iterated Cohen extensions and Souslin's problem, Ann. of Math. 94 (1971), 201245.
20. Steen, L. A. and Seebach, J. A., Counterexamples in topology (Holt Rinehart and Winston, New York, 1970).
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.
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).
23. Tall, F. D., An alternative to the continuum hypothesis and its uses in general topology (preprint).
24. Traylor, D. R., Concerning metrizability of pointwise paracompact Moore spaces, Can. J. Math. 16 (1966), 407411.
25. Traylor, D. R., Metrizability and completeness in normal Moore spaces, Pacific J. Math. 17 (1966), 381390.
26. Traylor, D. R., Metrizability in normal Moore spaces, Pacific J. Math. 19 (1966), 174181.
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.
28. Worrell, J. M., Jr., On continuous mappings of metacompact Čech complete spaces, Pacific J. Math. 30 (1969), 555562.
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On the Existence of Normal Metacompact Moore Spaces which are not Metrizable

  • Franklin D. Tall (a1)

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