Products with linear and countable type factors
Authors:
S. Purisch and M. E. Rudin
Journal:
Proc. Amer. Math. Soc. 125 (1997), 18231830
MSC (1991):
Primary 54D18, 54B10, 54D15, 54A25
MathSciNet review:
1415363
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Abstract 
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Additional Information
Abstract: The basic theorem presented shows that the product of a linearly ordered space and a countable (regular) space is normal. We prove that the countable space can be replaced by any of a rather large class of countably tight spaces. Examples are given to prove that monotone normality cannot replace linearly ordered in the base theorem. However, it is shown that the product of a monotonically normal space and a monotonically normal countable space is normal.
 [B]
Carlos
R. Borges, A study of monotonically normal
spaces, Proc. Amer. Math. Soc. 38 (1973), 211–214. MR 0324644
(48 #2994), http://dx.doi.org/10.1090/S00029939197303246444
 [BR]
Z.
Balogh and M.
E. Rudin, Monotone normality, Topology Appl.
47 (1992), no. 2, 115–127. MR 1193194
(94b:54065), http://dx.doi.org/10.1016/01668641(92)900669
 [F]
V.
V. Fedorčuk, Ordered spaces, Dokl. Akad. Nauk SSSR
169 (1966), 777–780 (Russian). MR 0208565
(34 #8375)
 [GH]
Leonard
Gillman and Melvin
Henriksen, Concerning rings of continuous
functions, Trans. Amer. Math. Soc. 77 (1954), 340–362. MR 0063646
(16,156g), http://dx.doi.org/10.1090/S00029947195400636465
 [H]
R.
W. Heath, An easier proof that a certain countable space is not
stratifiable., Proc. Washington State Univ. Conf. on General Topology
(Pullman, Wash., 1970), Pi Mu Epsilon, Dept. of Math., Washington State
Univ., Pullman, Wash., 1970, pp. 56–59. MR 0266135
(42 #1044)
 [M]
Kiiti
Morita, On the product of paracompact spaces, Proc. Japan
Acad. 39 (1963), 559–563. MR 0159302
(28 #2519)
 [P]
S.
Purisch, The orderability and closed images of
scattered spaces, Trans. Amer. Math. Soc.
320 (1990), no. 2,
713–725. MR
989584 (90k:54044), http://dx.doi.org/10.1090/S00029947199009895840
 [S]
M. Starbird, The normality of products with a compact or metric factor, Thesis, U. of Wis., Madison, (1974).
 [B]
 C. J. R. Borges, A study of monotonically normal spaces, Proc. Amer. Math. Soc. 38 (1973), 211214. MR 48:2994
 [BR]
 Z. Balogh and M. E. Rudin, Monotone normality, Topology Appl. 47 (1992), 115127. MR 94b:54065
 [F]
 V. V. Fedorcuk, On ordered spaces, Dokl. Akad.Nauk. SSSR 169 (1966), 778880; English Transl., Soviet Math. Dokl. 7 (1966), 10111014. MR 34:8375
 [GH]
 L. Gillman and M. Henriksen, Concerning rings of continuous functions, Trans. Amer. Math. Soc. 77 (1954), 340362. MR 16:156g
 [H]
 R. W. Heath, An easier proof that a certain countable space need not be stratifiable, Proc.Washington State Univ. Conf. on General Topology, Pullman, Wash. (1970) 5659. MR 42:1044
 [M]
 K. Morita, On the product of paracompact spaces, Proc. Japan Acad. 39 (1963), 559563. MR 28:2519
 [P]
 S. Purisch, The orderability and closed images of scattered spaces, Trans. Amer. Math. Soc. 320 (1990), 713725. MR 90k:54044
 [S]
 M. Starbird, The normality of products with a compact or metric factor, Thesis, U. of Wis., Madison, (1974).
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Additional Information
S. Purisch
Affiliation:
Department of Mathematics, Barry University, Miami Shores, Florida 33161
M. E. Rudin
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
DOI:
http://dx.doi.org/10.1090/S0002993997040264
PII:
S 00029939(97)040264
Keywords:
Linearly ordered,
countable,
monotonically normal,
product
Received by editor(s):
August 14, 1995
Communicated by:
Franklin D. Tall
Article copyright:
© Copyright 1997
American Mathematical Society
