|
Products with linear and countable type factors
Author(s):
S.
Purisch;
M.
E.
Rudin
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1823-1830.
MSC (1991):
Primary 54D18, 54B10, 54D15, 54A25
MathSciNet review:
1415363
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
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.
References:
- [B]
- C. J. R. Borges, A study of monotonically normal spaces, Proc. Amer. Math. Soc. 38 (1973), 211-214. MR 48:2994
- [BR]
- Z. Balogh and M. E. Rudin, Monotone normality, Topology Appl. 47 (1992), 115-127. MR 94b:54065
- [F]
- V. V. Fedorcuk, On ordered spaces, Dokl. Akad.Nauk. SSSR 169 (1966), 778-880; English Transl., Soviet Math. Dokl. 7 (1966), 1011-1014. MR 34:8375
- [GH]
- L. Gillman and M. Henriksen, Concerning rings of continuous functions, Trans. Amer. Math. Soc. 77 (1954), 340-362. 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) 56-59. MR 42:1044
- [M]
- K. Morita, On the product of paracompact spaces, Proc. Japan Acad. 39 (1963), 559-563. MR 28:2519
- [P]
- S. Purisch, The orderability and closed images of scattered spaces, Trans. Amer. Math. Soc. 320 (1990), 713-725. MR 90k:54044
- [S]
- M. Starbird, The normality of products with a compact or metric factor, Thesis, U. of Wis., Madison, (1974).
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
54D18, 54B10, 54D15, 54A25
Retrieve articles in all Journals with
MSC (1991):
54D18, 54B10, 54D15, 54A25
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:
10.1090/S0002-9939-97-04026-4
PII:
S 0002-9939(97)04026-4
Keywords:
Linearly ordered,
countable,
monotonically normal,
product
Received by editor(s):
August 14, 1995
Communicated by:
Franklin D. Tall
Copyright of article:
Copyright
1997,
American Mathematical Society
|
