Products with linear

and countable type factors

Authors:
S. Purisch and M. E. Rudin

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1823-1830

MSC (1991):
Primary 54D18, 54B10, 54D15, 54A25

MathSciNet review:
1415363

Full-text PDF Free Access

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.

**[B]**Carlos R. Borges,*A study of monotonically normal spaces*, Proc. Amer. Math. Soc.**38**(1973), 211–214. MR**0324644**, 10.1090/S0002-9939-1973-0324644-4**[BR]**Z. Balogh and M. E. Rudin,*Monotone normality*, Topology Appl.**47**(1992), no. 2, 115–127. MR**1193194**, 10.1016/0166-8641(92)90066-9**[F]**V. V. Fedorčuk,*Ordered spaces*, Dokl. Akad. Nauk SSSR**169**(1966), 777–780 (Russian). MR**0208565****[GH]**Leonard Gillman and Melvin Henriksen,*Concerning rings of continuous functions*, Trans. Amer. Math. Soc.**77**(1954), 340–362. MR**0063646**, 10.1090/S0002-9947-1954-0063646-5**[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****[M]**Kiiti Morita,*On the product of paracompact spaces*, Proc. Japan Acad.**39**(1963), 559–563. MR**0159302****[P]**S. Purisch,*The orderability and closed images of scattered spaces*, Trans. Amer. Math. Soc.**320**(1990), no. 2, 713–725. MR**989584**, 10.1090/S0002-9947-1990-0989584-0**[S]**M. Starbird,*The normality of products with a compact or metric factor*, Thesis, U. of Wis., Madison, (1974).

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:
http://dx.doi.org/10.1090/S0002-9939-97-04026-4

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