Normality in products of Rudin's Dowker spaces which are constructed from Suslin trees
Keywords:
Dowker spaces, Products of normal spacesAbstract
If $\kappa$ is the successor of an uncountable regular cardinal, $N$ a finite integer and $\left\{R^i\right\}_{i \in N}$ is a finite sequence of $\kappa$-Suslin trees such that $\prod_{i \in N} R^i$ has the $\kappa$-c.c., then $\prod_{i \in N} X^i$ is normal when $X^i$ is a Rudin's Dowker space that is constructed from $R^i$. Moreover, $\prod_{i \in N} X^i$ is again Dowker by the same assumption.
References
Z. T. Balogh, Nonshrinking open covers and K. Morita's duality conjectures, Topology Appl. 115 (2001), no. 3, 333-341.
K. Chiba, T. C. Przymusiński, and M. E. Rudin, Normality of product spaces and Morita's conjectures, Topology Appl.
C. H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951), 219-224.
R Engelking, General topology, rev. ed. ed., Heldermann, Berlin, 1989.
L. Gillman and M. Henriksen, Concerning rings of continuous functions, Trans. Am. Math. Soc. 77 (1954), 340-362.
L Gillman and M. Jerison, Rings of continuous functions, D. Van Nostrand, New York, 1960.
K. P. Hart, Strong collectionwise normality and M. E. Rudin's Dowker space, Proc. Amer. Math. Soc. 83 (1981), no. 4, 802-806.
T. Jech, Set theory, the third millennium edition, revised and expanded ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.
K. Morita, Products of normal spaces with metric spaces, Math. Ann. 154 (1964), 365-382.
K. Morita, Some problems on normality of products of spaces, General Topology and its Relations to Modern Analysis and Algebra, Part B, IV, Proc. Fourth Prague Topology Symp., Prague (1976), 296-297.
A. Rinot and R. Shalev, A guessing principle from a Souslin tree, with applications to topology, arXiv:2104.09150v2, 2021.
M. E. Rudin, Countable paracompactness and Souslin's problem, Can. J. Math. 7 (1955), 543-547.
M. E. Rudin, A normal space $X$ for which $X times I$ is not normal, Fund. Math. 73 (1971), 179-186.
M. E. Rudin, Souslin trees and Dowker spaces, Topics in topology, Keszthely (Hungary), Colloq. Math. Soc. János Bolyai 8 (1972), 557-562.
R. Sikorski, Remarks on some topological spaces of high power, Fund. Math. 37 (1950), 125-136.
P. J. Szeptycki, Normality in products with a countable factor, Topology Appl. 157 (2010), no. 9, 1622-1628.
H. Tamano, On paracompactness, Pacific J. Math. 10 (1960), 1043-1047.
