论文信息 - On δ-normality

On δ-normality

Abstract A subset G of a topological space is said to be a regular G δ if it is the intersection of the closures of a countable collection of open sets each of which contains G . A space is δ-normal if any two disjoint closed sets, of which one is a regular G δ , can be separated by disjoint open sets. Mack has shown that a space X is countably paracompact if and only if its product with the closed unit interval is δ-normal. Nyikos has asked whether δ-normal Moore spaces need be countably paracompact. We show that they need not. We also construct a δ-normal almost Dowker space and a δ-normal Moore space having twins.

Chris Good | I. J. Tree | C. Good

[1] Brian M. Scott,et al. Some “almost-Dowker” spaces , 1978 .

[2] M. Katětov. Complete normality of cartesian products , 1948 .

[3] T. Krämer. A note on countably subparacompact spaces , 1973 .

[4] P. Nyikos. A provisional solution to the normal Moore space problem , 1980 .

[5] Kenneth Kunen,et al. Set Theory: An Introduction to Independence Proofs , 2010 .

[6] Teodor C. Przymusinski. Products of Normal Spaces , 1984 .

[7] D. Burke. PMEA and first countable, countably paracompact spaces , 1984 .

[8] G. M. Reed,et al. Metrization of Moore spaces and generalized manifolds , 1976 .

[9] Gary Gruenhage,et al. Generalized Metric Spaces , 1984 .

[10] J. Mack. Countable paracompactness and weak normality properties , 1970 .

[11] J. Chaber. On subparacompactness and related properties , 1979 .

[12] Lynn Arthur Steen,et al. Counterexamples in Topology , 1970 .

[13] G. M. Reed. On normality and countable paracompactness , 1980 .

[14] C. H. Dowker. On Countably Paracompact Spaces , 1951, Canadian Journal of Mathematics.

[15] G. M. Reed,et al. On chain conditions in Moore spaces II , 1974 .

[16] Peter Davies. Nonperfect spaces with point-countable bases , 1979 .

[17] G. M. Reed. On Continuous Images of Moore Spaces , 1974, Canadian Journal of Mathematics.