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

DOI:
https://doi.org/10.1090/S0002-9939-97-04026-4

MathSciNet review:
1415363

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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]**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).

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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:
https://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