Geodesic
Even Covering Properties and Somewhat Normal Spaces
Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 154-159

Voir la notice de l'article provenant de la source Cambridge University Press

A topological space X is said to be somewhat normal provided that for each open cover is a normal cover of X. We show that a completely regular somewhat normal space need not be normal, thereby answering a question of W. M. Fleischman. We note that a collectionwise normal somewhat normal space need not be almost 2-fully normal, as had previously been asserted, and that neither the perfect image nor the perfect preimage of a somewhat normal space has to be somewhat normal.
DOI : 10.4153/CMB-1986-026-5
Mots-clés : Primary, 54D18, Secondary, 54D15 
Künzi, Hans-Peter; Fletcher, Peter. Even Covering Properties and Somewhat Normal Spaces. Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 154-159. doi: 10.4153/CMB-1986-026-5
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[1] 1. Asanov, M.W., Properties that are close to paracompactness, Math. Zapeski 9 (1975), pp. 3—9. (Russian) Google Scholar

[2] 2. Cohen, H.J., Sur un problème de M. Dieudonné, C.R. Acad. Sri., Paris 234 (1952), pp. 290–292. Google Scholar

[3] 3. van Douwen, E., Hausdorff gaps and a nice countably paracompact nonnormal space, Topology Proc. 1 (1976), pp. 239–242. Google Scholar

[4] 4. Engelking, R., General Topology, Monografie Mat. 60, Polish Scientific Publishers, Warsaw, 1977. Google Scholar

[5] 5. Fleischman, W.M., A new extension of countable compactness, Fund. Math. 67 (1970), pp. 1—9. Google Scholar

[6] 6. Hart, K.P., Strong collectionwise normality and M. E. Rudin’ s Dowker space, Proc. Amer. Math. Soc. 83 (1981), pp. 802–806. Google Scholar

[7] 7. Kljusin, V.L., On spaces with regularly refinable coverings, Dokl. Akad. Nauk SSSR 204 (1972), pp. 782–783. Soviet Math. Dokl. 13 (1972), pp. 740-742. Google Scholar

[8] 8. Mack, J., On a class of countably paracompact spaces, Proc. Amer. Math. Soc. 16 (1965), pp. 467–472. Google Scholar

[9] 9. Mack, J.E. and Johnson, D.G., The Dedekind completion of C(X), Pacific J. Math. 20 (1967), pp. 231–243. Google Scholar

[10] 10. Michael, E., Point-finite and locally finite coverings, Canad. J. Math. 7 (1955), pp. 275–279. Google Scholar

[11] 11. Moore, R.L., Foundations of Point-set Theory, Amer. Math. Soc. Publ. No. 13, revised edition, 1962. Google Scholar

[12] 12. Shapiro, H.L. and Smith, F.A., Even covers and collectionwise normal spaces, Canad. J. Math. 30 (1978), pp. 466–473. Google Scholar

[13] 13. Shapiro, H.L. and Smith, F.A., Paracompactness in uniform spaces, Topology Proc. 3 (1978), pp. 179–197. Google Scholar

[14] 14. Shapiro, H.L. and Smith, F.A., Neighborhoods of the diagonal and strong normality properties, Proc. Amer. Math. Soc. 71 (1978), pp. 329–333. Google Scholar

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